In the Blake-Gonzalez Olympic semifinal match, why couldn't they use the replay system to check for a touch?

Blake did ask if he could use the hawk-eye and the umpire said no; and I don't blame him as he has to abide by the rules which, like you said, state that it can only be used to challenge line calls. I think it's because they try to prevent players from abusing the technology (like when they decided to limit the number of unsuccessful challenges). It's a bit frustrating, but these things happen all the time and they are part of every sport.