You make valid points for why it comes off as bad but I did host a game where Cult could convert a Mafia, albeit it was a special type of Cult but Cult nonetheless. My experience with this is that the game was not too bad.I don't think it is particularly restricting on the host nor is it discouraging them to get creative. It is more of a factual opinion. On standard setups, recruiting mafia doesn't work with the overall flow of the game. You're giving access to the cult to someone who already has a variety of information about the mafia faction.
Not only that but let's say you allow the cult leader to convert a mafia player and that person is still participating in the mafia chat. The converted mafia player can both influence mafia's night actions to benefit the cult and also plan cult's night actions accordingly. Basically, mafia is now cult's branch. You can restrict the player to not influence the game but every restriction you add is a step towards hindering the flow of the game. On the other hand, even if the player does not talk in the chat, it is a fact they're still receiving a constant influx of information about mafia's actions and, if the converted player can't do anything with information he receives to either plan the night actions of the cult or lynch the remaining players, the converted player might start feeling discouraged and may even question the point of him/her playing.
For a game where a 'mafia conversion' is possible and is still balanced/enjoyable, the host should come up with a way to counter all those hindrances in a logical manner. Maybe an open 'chaos' game could allow this type of action but I'm not sure 'chaos' games can be called mafia games.
Now, there are a lot of creative people so if someone designs a setup in which these conversions are necessary and important for the game then it must be evaluated as an isolated case in order to see what counters the host has come up with,but for the rest of them, I still think converting mafia players to the cult is not a good approach.