A documentary at Radio-Canada named "mégastructures nazies" mentioned the Me262 as not being suited for a bomber role. Also, Albert Speer was against the decision to convert the Me262 to this role, as said in the book "Albert Speer : le confident de Hitler" by Benoît Lemay. But why was it not suited for this role ? I'm not very good in planes, I'm better in tanks, so I don't have the knowledge to answer it myself.
The basic reasons would seem to be that it can't carry enough, not having been designed to lift a significant bomb load, and that there weren't any bomb sights at the time that would enable a single-seat aircraft, flying very fast and probably low, to actually hit much with its few bombs.
It might have worked as a dive-bomber, but it would have needed significant modifications for that, and the Luftwaffe had mostly given up dive-bombing by 1944. Edit: The aircraft is much faster than the Ju 87, but I really doubt it could be dived at full speed, because it would have hit compressibility problems rather quickly. It would have needed powerful dive brakes, and would have been vulnerable to AAA in the dive.
I don't know why Hitler wanted a very fast bomber, but there are a couple of obvious possibilities:
The Junkers Ju 88 was designed as a "Schnellbomber" in the 1930s, when it was believed that a fast enough bomber could not be intercepted. There were short periods when bombers outperformed fighters, because the fighters were still biplanes, and a fast enough bomber can avoid fighters if it does not have to penetrate far into the defended zone and the defenders don't have radar to allow them to anticipate its arrival.
The Ju 88 did best of the German bombers in the Battle of Britain, and thereafter, but this is because it was a more modern and better-designed aircraft than the He 111 or the Do 17, and was superior to them in both performance and robustness. Hitler might have felt that performance was the key.
The other example is the de Havilland Mosquito, which was extremely difficult to intercept. The reason for this was that it was almost as fast as the German fighters (although not as agile) but had superior altitude performance, thanks to excellent streamlining and superior engine superchargers. However, the reasons it could hit anything with bombs were that it had a second crewman to aim the bombs, and advanced navigational electronics, which again needed a second crewman to operate. It was the most successful WWII example of the Schnellbomber concept.
The Me 262 is faster than the Mosquito, but has to carry its bombs externally, which costs speed and range, lacks an electronic navigation system comparable to the Mosquito, and overworks the pilot by requiring him to aim bombs and dodge AAA at the same time.
Bomb-sights that enable a fast and low-flying single-seat aircraft to bomb fairly accurately were invented in the 1950s, along with such techniques as "toss bombing."
Addendum: The Messerschmitt company did an outline design, as "Project 1100," for a fast bomber derived from the Me 262. The initial version of January 1944 used the wings, tail and engines of the Me 262, but with a new fuselage that accommodated a two-man crew, an internal bomb-bay and more fuel. Subsequent iterations of the project revised the wings and tail and allowed for more powerful engines. The project was ended in 1945, at the cockpit mock-up stage. Source: Luftwaffe Secret Projects: Ground Attack and Special Purpose Aircraft, Dieter Herwig & Heinz Rode, Midland Counties Press 2003.
John Dallman tackled it from the tactical perspective. I'll tackle it from the strategic perspective: would the Me 262 be a useful bomber at the time when it would have been available? Would it be able to fulfill its mission, and was that mission valuable? First some context.
The Me 262 made its first successful flight on 18 July 1942. At that time Germany was at its high water mark and they had reason to be optimistic. In the West the Atlantic Wall seemed solid. On the Eastern Front Army Group South was barrelling towards the Caucasus. The US hadn't committed ground troops yet and remained inexperienced and untested. US daylight bombing of Germany had only just begun and it wasn't going well without fighter support. The First Battle of El Alamein was raging holding the fate of North Africa in the balance. German U-Boats had just finished feasting on hapless US shipping.
By mid-1943 they were still working out problems with the Me 262's engine. The situation for Germany had changed drastically and they were now on the defensive. Bombs dropped on Germany had quadrupled, but it was still costly. The Sixth Army had been destroyed at Stalingrad and the Eastern Front had turned into a slow, grinding retreat. North Africa had been lost and the Axis were preparing for an invasion of Sicily. And the Battle of the Atlantic had turned dramatically against the U-Boats.
Germany won their spectacular victories, in part, from a head start in technology and tactics. They had lost this edge as the Allies frantically caught up and now their economic weight was telling. Germany wanted this advantage back. Hitler and Speer saw this in the Me 262, but they saw very different things.
A more sensible commander, under attack from all sides, would have taken a generally defense mindset and husbanded their resources for a counter-offensive. Not Hitler. He wasn't a trained, flexible military commander. Instead, he was a gambler and inflexibly offensively minded and increasingly focused not just on attack but on vengeance. In Hitler's mind the Soviets could still be beaten, and the coming invasion of Western Europe thrown into the sea, not with solid tactics, but with wonder weapons. Hitler saw in the Me 262 a high-speed tactical bomber for a dreamed new offensive and vengeance attacks.
But with Germany on the retreat, what would this new offensive be? And what were a few hundred light bombers carrying a thousand pounds of bombs going to do against the Allied avalanche?
Albert Speer, Minister of Armaments and War Production, saw Germany being dismantled from the air. He saw ever increasing production and fuel problems brought on in part by the air attacks. He knew this would only get worse and they were running out of time to stop it. Speer saw in the Me 262 a high-speed interceptor to sweep the Allied bombers and their eventual fighter escorts from the skies and let him get on with the business of supplying the German army and people. Any delay and it might be too late.
You can't have a bomber if there's no factories to build it. You can't have a bomber if there's no fuel to supply it. You can't have a bomber if there's no airfields to fly from. You can't have a bomber if there's no trained pilots to fly it. And you can't have a bomber if the sky is full of enemy fighters, doesn't matter how fast you are.
That last point is worth expanding. By 1944 long-range Allied fighters were available. Rather than simply defend the bombers, they began attacking German airfields in earnest. Rather than waiting for the Luftwaffe to come to them, they dismantled the Luftwaffe by striking them at home.
This revealed a fatal flaw in the Schnellbomber concept for Germany in 1944. Sure, you might be able to zip through enemy air defenses, drop your bomb load, and zip home... but what's the use if there's a flight of long-range Allied fighters circling over your airfield waiting to shoot you down? While on the ground refueling and rearming and getting an engine overhaul your jet bomber is as vulnerable as a piston engine aircraft.
What's the use of having a jet bomber if your pilots aren't properly trained because there's no fuel for training flights? Many inexperienced Me 262 pilots were picked off by well-trained and experienced Allied pilots flying inferior aircraft with more skill and better tactics.
That's why the Me 262 was not suited for a bomber. Germany desperately needed an air-defense fighter, not a bomber. The Me 262 did not have the range or bomb load to make a strategic impact; and Germany did not need a new tactical offensive weapon, they were on the defensive. And by the time it might have been ready in 1944 they had already lost control of the skies over Germany making all aircraft and their facilities vulnerable, jets or no jets. They needed an aircraft that could wrest air superiority back, and they didn't have it until it was too late.