The answer to that is difficult. It has to do mainly with technological limitations and fluid dynamics.
In fact, you should ask about time to flank speed, as this would be your only measure of maximum output shaft horsepower (shafts, actually). The power delivered to the shaft is just enough to propel ship at desired speed. For example,
HMS Canada could cruise at 14 knots using less than 18% of nominal power, yet reaching 22 knots required her full (nominal) power of over 38k shp (303 RPM). And during trials she exceeded 24 knots, at 52.6k shp (and propeller shaft RPM exceeded 335).
See "British Battleships of World War One: New Revised Edition" for more details.
Anyway, the problem at some point is water... Because at those speeds water is... well, hard would be one way of putting it. Another is: when one goes that fast it's not a lubricant anymore...
Another problem is cavitation, which was recognized well after 1960s, and which reduces the efficiency of powertrain.
And last but not least... With the exception of nuclear-powered ships designed from keel as such, ships' designs are optimized for cruising speed (which is not the max speed), and those designs are not efficient at high speeds. There are ways to alleviate that, but obviously older designs would be deficient in that regard too, sometimes greatly. This has to do with fuel consumption, which is not a concern for nuclear-powered vessels. So while it's not in your question, I would recommend to do any comparison on era-by-era basis.
So. By now you should see the problem with your question...
Typically battleships of that size (25-30k tons displacement) required about 50-60 min to reach maximum speed. They could reach maximum power only during max-speed runs, as power produced by the engines must be dumped somewhere, and you literally can't run ship's propeller shaft from start to 330RPM in no-time. It's same thing everywhere - when you want to burn tyres when accelerating in your car there are parts of the transmission system that would prevent engine from sending all it's power to the powertrain... There is a reason why new (that is new when they first unveiled the new generation) Nissan GTR had a caveat in warranty stating pressing "race mode" button voids it as it is likely to damage shaft.
And the numbers from opening paragraphs are - let's be honest - nothing.
USS Iowa, when on her trials, reached contracted 32.5 knots, what requried about 212k shp. And she was running light for that. How long it took is nowhere to be found (those numbers are classified), but since she was larger than
Hood (and heavier) it would be definitely longer. For some basic info on British ships see here, for stats on
Iowa here. CVNs have on hand even more: Enterprise was rated for 31 knots at 280k shp from 8 nuclear reactors, now Truman has 2 reactors outputting 260k shp.
[It is interesting to see that, for example, Scharnhorst required doubling of shp output to add just 4kt to already high speed of 26kt. This is the "water is not a lubricant anymore" issue at full display here.]
And one must not forget that
USS Iowa was built with designed overload of 20%, so we don't really know how fast really she could go. Same thing would apply to most WWII-era ships.
Last point to make:
USS Iowa was rated for power output of 158MW. That's slightly more than 80% of the
Nimitz Class CVs 194MW. Considering that both are rated at 30+ kts max speed, it shows the problems, limitations and solutions used: that a battleship with a full load displacement of a bit more than half of the 'Nimitz Class CV`'s (58kt vs 102kt) has that much power and is just a smidge faster than a CV?