Whops, I forgot to hit send on this one, so I'm writing this comment a tad bit late.
In DnD, helping others is limited to the Help action, which nobody takes because it's such a waste of an action. I wanted something to spice things up, something that made players feel like they were a tight group helping each other out instead of a band of mercenaries covering different grounds.
To do so, I looked at XCrawl's Mojo system, which this variant Inspiration is heavily based on. As with the original, it's designed as an incentive for bonding and roleplay, hence why you can only spend Inspiration on other players'rolls.
To simplify things, I did away with earning additional Mojo/Inspiration points and losing Mojo/Inspiration on a nat1: instead, the players have a single Inspiration point every day, that they can spend to help other players in a clutch.
The "no beggars" limitation is also lifted wholesale from XCrawl. I really like it because it awards players for staying alert during their fellow party members's turn.