Leicester, Southampton and Leeds coming back would be bad news for Everton in their state. If those three come back up they should have more money to spend than the likes of Burnley/Sheff U/Luton. Leicester are for sure better than Everton IMO even though they wouldn't be winning games like this every week in the Prem.
It's hard to judge. Burnley are the cautionary tale of a team that walked through the Championship but look dreadful against Premier League opposition, that despite spending £100m in the summer.
Some of these players may have been underachieving but Leicester have pretty much the relegated side minus internationals like Maddison, Barnes, Castagne, Tielemans, Perez, Soyuncu, Evans etc. Their big signings were Harry Winks and Connor Coady! Like Burnley they are playing possession based football and working out from the back against teams that are generally a bit... crap.
I agree though that three clubs with Premier League setups and fanbases coming back up would be bad news for Everton. Hoping that there's always three teams worse than yourselves is fine until the season comes along when it's not the case anymore.