That would be a real killer as far as getting new people to join. They would be told to check back in a few weeks. Many would not. It really helps to let people start playing and arranging their lineup and playing a game, even if they don't really understand training, or perhaps don't even know that much about basketball.
I could see some things that they might consider doing though. Perhaps late season joiners could be placed in "expansion leagues" outside the pyramid structure. These leagues might have no playoffs simply so that there are more regular season games. All teams would start with a 0-0 record, and it wouldn't matter much that there wasn't time for a balanced schedule. At the end of the season, these teams, who would all be of about the same vintage, could have a draft; and then after all the regular pro/rel was done be placed in their first regular season league.
This reduces the risk of a team replacing an abandoned team with a good record, accidentally promoting, and then becoming a bot themselves a couple of weeks later. It also reduces the chance that a team will take over an 8th place team that has zero chance of avoiding relegation.
Another possibility would be to fill whole leagues at a time, and starting teams with a 0-0 record even with just a few games in the season left. The teams that promote will be those that figure out the game quickest, not the team that inherits the record of a team whose players have been retired.