Michael
What you actually seem to be asking for is the creation of an entirely new type of league. Leagues can be password protected for different reasons and not just for the sake of having it as a private among a few friends.
For example a league host may only want to open a league up for new entrant's in the off season, as joining mid season can put a player at quite a large disadvantage, or maybe there is a waiting list to join the league as spaces are reserved, or the league runs special rules but is still for everyone but requires you to get in touch with the host first.
Also your suggestion open's up the possibility of somebody effectively freezing their account out of the leagues open structure if they join a private league without understanding the consequences. Which would produce additional administrative work.
The way I see it, I have sympathy for your suggestion as I can understand you wanting to make use of higher tiers and greater car design options, but the amount of work required to make what you are suggesting a reality is probably more than you are estimating, and certainly would not be a priority piece of work even if it was accepted.
So as a suggestion to get where you want to be, you should consider entering the open league system for a bit, getting yourselves promoted to pro or elite that way, and then re-entering your own private league afterwards. You will retain the tier that you are in when moving between leagues.
This suggestion is for those who decide that they just want to play together with their teams, and they do it together, so there would be no hasty private team transformations and i think there wouldn't be administration problems.
And you could play in a private league with a non-private team, only the other way around not, and as I already wrote, the entire category can only move up to the next category if all teams in the given category are private.