Awesome thread!
The Cleveland Barons were (as you read) one of the top teams in the '50s. Any expansion of the NHL from six to seven is likely going to necessitate an eighth team. It's also, as you point out, more likely that the NHL would introduce more teams into the league via. expansion if Cleveland is allowed in. IIRC during the Original Six period there were numerous teams trying to break into the league. I know a group of businessmen bought the rights to the dormant Montreal Maroons franchise and tried to "Balsille" their way into the league, but failed. Los Angeles and Cleveland constantly tried to gain entry but they had a pretty subjective review process that clearly stated their opposition to allowing them back in.
If the owners in Cleveland lobbied the league harder and threw them a few financial bones, it's very possible they could've been allowed into the league. Had they been allowed into the league into the '50s, the NHL would've been significantly changed. Cleveland had quite an incredible team. Johnny Bauer would likely be mentioned as a top 5 goalie all time up until the '90s (when who knows who comes around ittl) and Fred Glover would've been one of the stars of the "Original Seven" era.
In terms of expansion, going back on what I just said I think we'd likely see a brief "Original Eight" from 1954-'63/'65. An eighth team would probably be added to balance the schedule. Top contenders for that would be Philadelphia, if that group had put together some better financing, St. Louis (Wirtz owned the arena there) or Los Angeles (would make travel awful but it's not completely unthinkable). I'd wager it'd be Philadelphia -shrug-. The NHL would probably follow expansion patterns more like the MLB/NFL, adding a few teams in '63/'65 and every 2-4 years thereon adding anywhere between 1-4 more.
Another interesting scenario would've been if the NHL decided to allow Red Dutton and his New York Americans to rejoin the league in 1946. The Americans folded during WWII but according to Dutton they'd agreed once the war ended they'd reinstate the franchise. He'd supposedly got $7 mil to finance a new arena in Brooklyn but was outmaneuvered and lost his franchise. Had they allowed the Americans back in it I think they would've eventually wanted to add in an eighth, which could've been the Barons had it been done in the late '40s/early '50s.
That would probably make the NHL almost unrecognizable today, it'd be pretty interesting to speculate on how it'd look with a second New York team and Cleveland for the vast majority of its post-war history.