Richard's due as a general is not the problem, the fact that he wasn't as good a king as he was a general is the problem, so his deserved credit for the former is irrelevant to our discussion.]
Irrelevant only if he isn't a war leader at all, which is unlikely. Almost all European kings of Richard's era led their armies in person some of the time, including all the English kings from William I to Richard.
From the viewpoint of the 21st century, we can say that his energies would have been better spent on campaigning somewhere other than the Holy Land. People of the late 1100s, however, thought crusading was the highest cause possible, the kingdom of Jerusalem would have been in dire shape without Richard's intervention and none of the other crusading kings seem to get the same amount of criticism for crusading as Richard does. Plausible tweaks which affect England that could have happened in the Holy Land: (i) Richard doesn't make an unnecessary enemy of Leopold V of Austria; (ii) Richard and Philip leave together.
Because there's no way Richard can do anything other than the kind of things he did OTL?
Not sure what you're suggesting. I can't see Richard having a peaceful reign, if that's what you mean. No way he would have accepted French encroachments in Normandy or Acquitaine. If Philip kept the peace, I can imagine Richard campaigning in Scotland, Ireland or Wales instead.