A real pyramid structure has to go down to the very bottom of local football. If, for example, the HL champion gets promoted and no team is relegated into the HL, the place is filled from below, as the bottom team(s) are relegated to the local leagues and the winners of those get promoted to the HL, with play-offs of the second and third bottom HL sides and the runners-up of the local leagues for as many spaces as necessary.
BTW, that's the way the whole thing has been run in Germany and Austria since WW2. For example, German Bundesliga side Hoffenheim were in the second bottom local tier in the mid-80's, before they started their climb through the stages and ended up where they are now. Not through application and buying in, but by winning one league after the other and getting promoted to the next one. Sponsor Mr Hopp wasn't involved until around 2000...
Maybe AFC Wimbledon is another potential example stalled a bit at the moment but with those fans they will recover.
Ross County and ourselves made it
I remember myself watching Wigan Athletic in The Lancashire mid-week cup final , not that long ago they lost too to Rossendale United.
Who knows what the future holds.
NB The Quote thingy was not working to I had to adapt the post from above