I have to say that is exactly the opposite attitude to me and I would welcome them into the league.
One of the benefits of the pyramid system is that it rewards achievement, and if Bromley/Solihull or anyone else is good enough, then they should have the chance. After all, *we* had to 'apply' to be allowed into the football league initially - and the attitude that 'well they aren't an old school league club so we won't let them in' would have completely scuppered us! It's better now clubs get there on merit. I'd imagine there are fans of Prem clubs looking askance at the likes of Bournemouth or Brentford (both safe for another year) and saying they aren't 'proper' top flight clubs. If the 'proper old clubs' (who often have a bigger fan base than some of the smaller clubs) can't use their advantages well enough to get out of non-league then that's hard luck. One of them (Luton) have managed to resurrect themselves from non-league and get into the Prem within 10 years (much as I dislike that particular club).
There's a difference though between recognizing a club deserves to get into the football league because they've put together a great team on the field, and wanting other clubs to get back into the football league because they have the fans, tradition and infrastructure.
Since promotion from the National League to the EFL became automatic in 1986, the biggest and most successful club to emerge from non-league are Wycombe....a team that we still love to deride as being hilariously tinpot.
This year, there were five of those post-1986 promoted clubs in League One (Wycombe, Stevenage, Cheltenham, Fleetwood & Burton). Want to hazard a guess at who the five worst supported teams were? Yep, it's them. And none cracked an average of 5,000.
And there were eight post-1986 promoted clubs in League Two (not including AFCW because of their history, but including Barrow because they were a non-league club for half a century) and once again, they're occupying the bottom eight slots in the attendance table - Morecambe leading the way with 4,002. Meanwhile the three old school league clubs that had long stays in non-league before returning in the last couple of years (Wrexham, Notts County, Stockport) all averaged 9,300+
Football is just more fun when there's more opposition fans. And all the data suggests that the traditional football league clubs have them whilst the new breed don't.
Which is why we can recognize that either Bromley or Solihull deserve to get into the EFL.....but still cheer the fact that Sutton & FGR are going the other way, and hope that Oldham & Southend sort themselves out and return soon.