It's a fun feature, I agree. But it would have to be right after (for instance, during the first week) the draft or the creation of the team.
I totally agree with this. I have long advocated that every new team should be able to name a player and a position. This would then be created as an 18 year old all-star potential with somewhat random skills and height but suitable for their position. This would not unbalance the game at all but would give every new team a player they can identify with right away and encourage them to keep on playing at the possible cost of the game having a lot of Kobe Bryants running aound.