I currently don't have any of the unlockable characters (Mirage, Octane, Caustic, Wattson) and today 2 of my 3 dailies were for one of those characters, and one of my weeklies is for using one of their special abilities and they can't be completed any other way.
Challenges should only be generated for characters you have unlocked at the time; so they should either be generic ("Get 10 kills" or "Revive squadmates 5 times") or for characters you have access to (the free ones or any you have unlocked through gameplay/credit purchase) so you are able to complete all of them without playing a lot to unlock someone or needing to pay.
This is frustrating for a free player, and I can imagine it would be even more frustrating for anyone who has put money into the game.
Whatd you just download the game yesterday? Just play for an hour and youll get what you need. Dumbest complaint you could possibly make