Yeah but we don't know what's happened there. He might completely hate Koeman or club officials and be miserable despite playing regularly and at his level. Sometimes a change is needed just for a change. He's been at Everton his whole life and a first team regular for 4 years. If it was me I don't think I'd spend my whole career there.
And realistically, if you're not at one of the top 5/6 rich clubs and going to be consistently playing in European competitions then does it really matter if you're at the one that finishes 7th or the one that finishes 9th? My guess is that Everton will never reach the level of the clubs above them (even with investment) and Barkley's going to have a relatively mediocre career and never reach great heights so whether that involves spending 10 years at Everton or 4 years at Everton and 3 years at West Ham and at Leicester probably makes little difference.
Fair play to him though if by new challenge he means going abroad to really try something different, though I'm guessing he'll ask for more wages than he's worth and end up somewhere like West Ham that'll pay it.
I wouldn't be surprised if he ended up being another Sissoko at Spurs. A buy for the sake of it late in the window to look like they're actually doing something positive rather than nothing.