Operation Foxley was put together by the British in 1944, but eventually called off because a successor to Hitler could possibly be a better strategist and therefore make it harder for the Allies to win the war. Hitler would've become a martyr for the Nazi cause, which also would not have helped the Allies in any way.

So, yes, you could argue that the Allies 'allowed' Hitler to live. Suggesting that they did so to "prolong the punishment and destruction of Germany" is completely ridiculous and bordering pseudohistory though. The Allies' main concern was shortening the war and preventing friendly casualties.

Most of the allied bombing was intended to destroy Germany's manufacturing capability. If Germany was unable to make ammunition, tanks, planes and other weapons in sufficient numbers their ability to fight would be severely restricted.

Bomber Harris (chief of RAF Bomber Command) did believe that widespread bombing of cities could break the will of the people, hence attacks on major cities that caused devastating loss of life and left cities simply unrecognizable.

As far as I know there were ever bombing attacks that targeted Hitler, the Allies did attack the Berghof but this was in the last days of the war and was more about destroying the building than attempting to attack Hitler - IIRC it wasn't actually bombed until he was already dead. So, in a way I guess they did allow him to survive, but I would suggest that its for the reasons /u/kitarn gives.

Bomber Harris might have believed bombing cities was an effective tactic in 1942 but he surely knew otherwise in 1944. In WWII the Allies were firebombing cities killing tens of thousands of German and Japanese civilians monthly (and sending bomber crews into peril) with little effect on enemy morale or production. As for punishing Germany, remember that the blockade of Germany was maintained for eight months after the November 1918 armistice leading to possibly 100,000 deaths. Seems to me that both sides in both world wars purposely targeted civilians possibly for the purpose of assuaging their own civilians for the losses they had suffered (i.e., men in the field).

Though the other named factors are correct one factor that hasn't been mentioned is how for the most part it would have been extremely hard to pinpoint Hitler's location. His usual residences would be extremely hard to reach for the allied bombers.