As a coach now it remains to be seen. Maybe he has developed himself and grown up in the two years, but he didn't do so well at Everton either. The club now wants to see what happens and then decide, but I believe that they would prefer some well experienced professional coach. But who would be willing to take that job?
I think Todd Boehly is been smart here with his appointment of Frank Lampard, let say things were to get worse and we didn't win the champion league and also don't make the top 4 by the end of the season, that means we won't be playing champions league football next season and the club will automatically become unattractive to managers especially the top ones that the club has been linked with. If that was to happen then we'll have to work with Frank Lampard by just promoting him to the head coach of the club. Frank Lampard loves Chelsea and will definitely take the job knowing he won't be under much pressure and won't have other league distractions.
Frank Lampard is a builder and he has helped Chelsea once when we had financial issue that we couldn't sign players in the transfer window, Frank Lampard worked with the academy to promote some players that are now enjoying first team football today. I don't doubt Frank Lampard ability to build a team no body will want to to play against like the 2020/2021 team that won us the title although not under him but he built that team. I just hope he has improved on his players management skills so he can work with the current squad to get something to smile about this season.
I think the first point you made is a good one! Now that it doesn't look like they will make it into the Champions League, nobody can expect them to sign the best of the best as a coach as they won't be coach for a year without any European competitions whatsoever. From that perspective it was the right choice and actually, if for some weird reason they make it into the final this year and in the unlikely case that they win it, they immediately have a coach who is then familiar with going the whole distance (or at least the hard part of it). I think it is true and the players will respect him more than Graham Potter. Graham Potter I think neither has something to show as a player nor does he really as a coach. Lampard was a damn good player and he has some experience as well as a coach. On top of that he won't be asking a Guardiola-like salary.