Hmm... you are basically quoting almost every single major character. I can live with Kaladin and Dalinar and maybe Adolin, but I think it would be a very boring story if all of them became radiants.
I don't think having Shardblade/plate is necessary in order to become a 'Radiant'. Like it's been said, they are probably tainted, so there is a good reason for the Radiants giving them up, and maybe there was some secret power acting over Kaladin not wanting to take the Shards and Syl disliking them, and Dalinar feeling the urge to be rid of them.
I believe it's possible that Syl is kind of like the soul of a lost radiant, wandering about looking for someone worthy enough to carry the legacy of her powers, until she found Kaladin.
