...why was the Deutschland not sent on commerce raiding missions as opposed to larger battles?
Bad timing, and a bit of bad luck. She wasn't "less effective" by any means (other than being somewhat lighter build than her sister ships), she just did not get a chance at that one good raiding sortie that her sister ships had.
I'll mis-use the quotation markup here -- normal text on Deutschland / Lützow, quoted text on her sister ships and general course of the war.
At the outbreak of the war, Admiral Graf Spee was already in the South Atlantic, where she could immediately engage in commerce raiding -- in summer conditions. Admiral Scheer remained at anchor close to Wilhelmshaven.
The Deutschland had a short first stint as commerce raider in the (stormy, at this time of year) North Atlantic, during which she sank two ships and captured a third. She was then (November 1939) recalled for refit, including a new bow section to increase her seaworthiness. (Both the Deutschland class cruisers and the Scharnhorst class battleships had issues with wet foredecks, in part because they were lying so low in the water, in part because their bow section proved to be inappropriate for the North Atlantic.)
Admiral Scheer went directly from anchorage to refit. Admiral Graf Spee would have required refitting as well, plus an overhaul of her engines. After all, she had sailed to Madagascar and back. But in December 1939 she had already met her fate in the Battle of the River Plate, ending her stint after nine ships sunk (if I count correctly).
In March 1940, the refit of Deutschland (and her renaming to Lützow) was done. But Operation Weserübung was up, and Lützow was ordered to participate in the operation.
Admiral Scheer was at that time still undergoing refits, and would not be able to sail again till July.
During the invasion of Norway, Lützow took heavy damage in the Battle of Drøbak Sound, and had to return to port for repairs. Those took until the end of March 1941. In June, she was to sail to Norway, to eventually return to the Atlantic for raiding.
This was the time when Admiral Scheer was conducting her stint raiding in the Atlantic, sinking 17 merchant ships before returning for an overhaul of her engines.
As bad luck would have it, en route to Norway Lützow was hit by a torpedo bomber rendering her dead in the water, so she had to be towed back to Germany and repaired again. This would put her out of action till May 1942.
By summer 1941, raiding in the Atlantic had basically become impossible. The sinking of the Bismarck had proven how dangerous air superiority at sea was for capital ships. The network of supply ships that had kept the Kriegsmarine units fueled, fed, and armed was no more. Scharnhorst, Gneisenau and Prinz Eugen sat holed up in Brest under frequent air attacks. (The British joked about the "Brest Bomb Target Flotilla".) This led to the decision to recall the capital ships to better defendable waters (Unternehmen Zerberus, the Channel Dash). They would not return to the Atlantic for the rest of the war. Instead, they were relocated to Norway, to attack shipping there.
None of the German capital ships had significant success in the Norwegian Sea. The situation had changed. Instead of scouring the wide open waters of the Atlantic for lone merchants, the mission now was attacking escorted convois under Royal Navy air cover. The days of the lone raider were over -- not that any surface ship ever got a second stint in the Atlantic -- and so, eventually, German capital ships were either sunk, or retreated to the Baltic Sea.
(Sources: A mere reshuffling of the Wikipedia articles linked in the question, based on what I already knew about their timelines.)