As an optional mechanic, Inspiration is fine. A lot of players don't like the "DM may I?" approach to advantage, and handing out advantage to players so they can get it when they need it, without pestering (or worse, arguing with) the DM isn't a big deal.
If players forget they have it, that's kind of on them, since again, I see this as a shorthand for giving you advantage without having to have a discussion about it. And it's nice to have a reward other than xp, since I kind of like having all my party members be the same level when I run games (it's not strictly necessary, but I don't have any compelling reasons to stagger advancement), and so I don't hand out bonus xp very often.
And yes, as pointed out, poker chips or other physical reminders are pretty easy to hand out for forgetful players.
If I have an issue with Inspiration, I guess it's that it's kind of boring. I preferred Action Points (or the very similar Hero Points used by Pathfinder), and honestly think they would be more fun for players.
I can't see how it would be very broken either, since Action Surge is a thing, but I'd have to try it out to be sure.
All this having been said, I'm not sure why we're on about Inspiration anyways. If we wanted to discuss rules elements that don't quite cut the mustard, I'd bring up Alignment, Backgrounds, or those fiddly little roleplay things on the character sheets like Bonds and Flaws that never seem to come up in play.
Or my biggest (non-optional) pet peeve: what to do with all that treasure anyways?