Fair warning, bringing this topic up is going to lead to a great deal of technical quibbling over just how good the Tiger I and Tiger II were. I'll do my best to avoid that. I'll also avoid discussing their portrayal in games and films, since those depictions reveal more about their creators than they do about actual history.

Tiger tank commanders knew they had a capable vehicle. Although it had its flaws, the Tiger family had excellent firepower and good frontal protection. And talented commanders made good use of these qualities. Some commanders took rather dramatic risks, counting on the Tiger's strengths to get them through. The fighting in Normandy during June and July 1944 offer some good examples of how such boldness could lead to success or to disaster.

Michael Wittman's famous engagement in Villiers-Bocage on 13 June 1944 is an example of a Tiger commander's rashness (or luck) paying off. Michael Wittman destroyed five British tanks in a matter of minutes, spearheading a counter-attack that badly disrupted British offensive operations.

But less than a month later, Wittman would be dead, killed after he lead his tank section in a mad dash towards British lines. In doing so, Wittman exposed his tank's flank to a British Sherman Firefly. His Tiger and two others were destroyed within minutes.

*Stephen Hart "Sherman Firefly vs. Tiger"

This is not so much an answer as a refutation of the question. I'm not quite sure why you believe that being confident in the quality of their tank would cause crews to hurl themselves to their deaths in reckless attacks. The Tiger was designed as a long-range tank destroyer. The crews were well-trained, often experienced, and knew that the strength of the tank lay in ranged gunnery. They had no intention of throwing away their advantage by moving in to close quarters and into ranges at which Allied weaponry could actually have an effect. The fact that Michael Wittman's actions at Villiers Bocage have been so well publicised indicates to me that they were out of the ordinary and did not represent the tactics usually used by Tiger commanders--whereas accounts of Tigers knocking out Allied tanks at long range are relatively common. And Wittman was extremely successful on that occasion, so it hardly represents a case of overconfidence in the vehicle; his success surely shows that his confidence was justified.

It seems to me that you're thinking about this the wrong way round, and trying to second-guess how they 'should' have acted. Rather than assuming that confidence would lead to rashness, we should see what tactics Tiger commanders actually used, and if we have evidence they 'went rambo' then we can try and explain why.

You see this happen with just about any tank, for any number of reasons ranging from battle fatigue to bad judgement.

The tactic would only work if the Allies were caught with their pants down. Even M4 Shermans with 75mm guns could penetrate the Tiger given sufficient range. Such exchanges were not what the Tiger was best at anyways- heavy tanks typically fit into the doctrine and role of the breakthrough tank which would fight with as much distance as possible to build a "wedge" other tanks could exploit.

Hell, one of the first times the Western Allies encountered a Tiger heavy tank, they defeated it by a lucky shot from a Churchill armed with a 6 pounder managed to get a round lodged in the tank's turret ring, forcing the crew to abandon it.