@AjikaOfficialSO after a little testing...
say you have dynasty A. It's going good with the people you're running with, but you want to have your own dynasty with TB teams, but you're at the limit of teams you can DL. You CAN delete teams from your device once the dynasty is under way and it'll have no effect on the look, logos or team from what i can see IN DYNASTY A... They just obv won't be available for play now games once you give em the boot.. Gives you the option in case you want to scuttle some less good looking schools out in a DYNASTY B and you're worried about pooching your A... I put in 10 TB teams in new Dynasty B, ran a game... deleted the 10th team from my device. Started dynasty B again... Simmed up to game with 10th team, launched game and verified all unis, stadium info and etc we're intact in dynasty after deletion AND verified that dynasty B didn't re-install 10th TB team onto HD upon launch...
This is nice, as it allows me to replace a corrupt team on my HD for a better one i created later...
As for reaching your '15' (16) DL limit... Did you happen to DL a custom playbook or sliders? I wanna say that it may count against that total but i could be mistaken...