I assume you try to set conditions somewhat similar for new teams. That is, their players are at least nominally comparable. They have the same amount of cash, arena, etc. This is simple fairness.
But they take over the record and schedule of another owner. Please understand, I'm not whining about my position, but simply using my team as an example. The original bot was 8-1. Then the first owners were assigned in mid-season. My team's first human owner was 1-9, losing by an average of 27 points per game. I won the last 3 games. Overall, at 12-10 I was tied for 5th best record in the league, but because of the point difference, I was 6th in my conference and facing relegation. If there had been one team placed in D.V, then I could have been relegated. I won 2 of 3 to take the series, with the only loss in 2 OT. 10% of my season ticket holders left the team. Had it not been for the fluke of a very good bot, my team would have been mired in 8th place.
All the teams in my league had 3 or 4 names last season, the original bots for 10 games, followed by a first owner, and then one or two new owners. I think with 3 league games, I am one of the veterans. And because of the bot cleanup, there are only 8 active teams in my league. Had there been a LSL, you could have filled as many D.IV leagues as possible from the LSL's, just as you filled all the D.III leagues from D.IV (or you might have even been placing the best teams from the LSL's into D.III).
Starting out, I would rather have been placed with other owners who were starting out, with a 0-0 record, and let us try to understand how games are played. Perhaps start looking at training or the TL. Bunches of those new owners will do zero. But in a way that is good, since the teams that do actually try the game will be relatively successful.
I don't understand why you say that owners who enter the league late will be at a disadvantage. With small leagues, you will fill each one within days if not hours. It is intended that those who enter very late, say when there are only time for 4 games to be at a relative disadvantage, to teams who played 10 games. But they won't be in the same LSL. You fill each LSL as quickly as possible, and then create another one. You don't refill.
Another way of looking at it, is as if you told people who signed up late in the season, that they were going on a waiting list, but while you're on that waiting list, you can start playing games against other teams. And we will use that performance to place your team at the start of the new season.
I agree that a freshly reset team won't be much of a challenge for established teams. But that is part of the problem. Some of the established teams will have played the previous team on autopiliot (which may be reasonably good - a bot took my league championship), and some will play the new owner.