McDavid still would have went to the Oilers, but they'd have been on the clock right away. The early years of Edmonton not making the playoffs or being a terrible team and being out immediately would have lead to them likely losing McDavid in 2020 or 2021. So they still would have had a chance, but upon failing, they would have likely lost him.
I see both sides of it. The risk is turning into the NBA where player movement is everywhere and building a small market team takes a stroke of luck... like Joker or Giannis. On the flip side, the league is limited because some of the biggest stars play in markets nobody really cares about. If Makar was in Toronto or LA, he'd be a much, much bigger name name outside the hockey world.
I wouldn't say it is 100% the case of the rich getting richer though... baseball is very much a rich getting richer sport and they have some of the longest restrictions on tenure. The cap would put a limit on it. There would certainly be less parity than today... and alongside that markets like Winnipeg, Arizona, Carolina, Florida (maybe... the right owner could get all the Russians), Isles, Sens, and Oilers would all have issues surviving.