This. If the PL is an arms race, Arsenal getting 4th just gives them a huge lead over us in terms of having access to top tier players to solidify their advantage over us, while we have to scrabble around for those content to play EL football.
And they spent 120m net this summer, without any European football. If they get into the CL and repeat that level of investment, plus CL revenues, plus having a *lot* of slack on the wage bill to take up (all their highest earners are gone and have been replaced by youngsters on low wages), we could see them spend an absolute brick-ton this summer and lock us out for the foreseeable future.
This is the worry. This is why finishing above them and keeping them out of the CL is vital.
It wouldn't matter as much if we had an owner like Kroenke who would invest in the club whether or not we're in the CL...but, well, you know. We can't match them, nor most of the other PL teams, in terms of having owners who care about their clubs being competitive.
So we have to deny other teams advantages over us. And Arsenal finishing 4th is a huge one for them.