I don't think that having more awards would make Billy Crystal's legacy better or more important. There are plenty of people who don't get awards that are very important to the culture. I think that it would be nice if he got some, but it is not necessary for his career.
No, I do not feel that Billy Crystal deserves a lot more award than he's actually received, because Billy Crystal has not been shorted when it comes to awards. Crystal actually hasn't done that much in terms of blockbusters movies in a while. He has won recognition for his past works.
Billy Crystal is a good and accomplished actor, but he should not be ranked among the all-time greats in film. How many films of his can you name off of the top of your head? This speaks to the fact that most of his films did not cause a big impact, either commercially or culturally. While he is a good actor, his films have had limited impact.
Billy Crystal has been in some great, classic movies that deserved some recognition and he received a lot of praise for those. However, he hasn't really done much in a long time worth an award. I haven't seen him take on any roles outside his comfort zone that would really stretch his talents. He is a solid actor but never really plays it big. I think he has received just the right amount of awards for those efforts that were his real masterpieces (i.e. When Harry Met Sally).
Comedy often gets the shaft when considering awards, so it's no surprise that Billy Crystal has not receive a lot of awards. I don't think this stance needs to be changed and I don't think Billy Crystal deserves more than what he has received. It is what is, there's no need to hand everyone a trophy.