No need for flash in Generation 1 dark cave but I don't think you can see items or trainers without it. Generation 2 is useful since you can't even see the outline of the path and I'm not wasting my time trying to get through it without flash. Atleast theres a move deleter. And for Generation 3, Flash is pointless if you either know where you're going, or if you have a lot of repels and you can do some trial and error.
And Cut isn't really a BAD move... isn't it better then scratch? Strength and the otehr HM's (minus whirlpool, i hate it) are pretty decent atleast in my opinion.