I think Europe doesn't need many more spots than it already has, maybe one or two. In the 90s\early 00s before most EE teams hit a significant decline then it would have been good, but how many 2nd and 3rd tier UEFA countries have had memorable tournaments since?
The turks in 2002. Ukraine got to the quarters in 06 but were mostly awful and quite a bit worse than their late 90s\early 00s teams that lost playoffs. Portugal 06 but they were really closer to being among the best then tbh . Belgium 14, though they were mostly poor to watch. Maybe you could argue the Netherlands of 2014 had regressed far enough to be considered 2nd tier doing well.
I'm sure i've forgotten one or two, but there isn't many more. 2nd tier and 3rd tier euro teams are usually just as erratic\flawed as the better African and Asian teams. You rarely see any overperform.