The transfer market helps them too. Bigger clubs can't get away with signing anybody, they have to get stars to appease the fans and sell shirts. Leicester don't have the same pressure, they have choices from which they are able to sign players for meaningful reasons, and once they arrive the manager knows exactly what to do with them.
Yes, this is also true - in a weirdly paradoxical way, having less money can sometimes be a benefit, although it also means that you lose your best players to bigger, richer clubs on a regular basis. Something that Klopp knows only too well.
But all things considered, I think I'd still prefer to have loads of money to spend on players and wages. Because most players view the smaller clubs as a stepping stone and play out of their skins to expedite that move to bigger clubs and higher wages.
We're more fortunate than most, in that we're a big, rich club anyway, and there's only a handful of teams that players would want to move to: Bayern, Barca, Real, PSG, City, Chelsea (maybe) and arguably Juve, Inter, Dortmund but that's about it. We can't afford to allow clubs like Spurs overtake in that particular pecking order, although from a wages POV that is very unlikely until they get their new stadium.
At a level below us, you've got teams like Everton, who know that they are unlikely to keep their very best players for long if they stay fit and on form, so Lukaku, Barkley and Stones will probably all leave sooner rather than later, with Rooney being the best example.
