A huge benefit of saving throws is that each player rolls hiw own die or dice, and modifiers applied to the conditions of your own figure(s) are applied to your own roll. Not all gaming engines do that, but having two rolls is an excellent mechanic to implement that idea. E.g. cover should not be a negative modifier on the shooter’s roll, but should be a positive modifier on the target’s roll.
Another benefit, as has been pointed out already, is that both players roll, and you take ‘ownership’ of part of the procedure.
Much of the dislike of the saving throw in some circles has to do with the narrative. ‘I did hit you already, and now suddenly you’re ok?’ So change the ‘explanation’ of the saving throw to suit your own needs.
Some relevant posts on the wargaming mechanics blog:
Tiny Tin Men Blog: http://snv-ttm.blogspot.com/
Wargaming Mechanics Blog: http://wargaming-mechanics.blogspot.com/