No not at all. It's clear that you didn't study the development of his character properly. It's not always about being tough as nails, cold, ruthless, and near-invincible when it comes to GTA protagonists, despite the brutal nature of their criminal careers. Sometimes a good dose of real human life elements are what is needed to develop a character, and that does not always involve being the ultimate hard man.
CJ's was portrayal was supposed to be one of a vulnerable and emotionally fragile young guy that struggles to eventually overcome all the obstacles he faces in his cold, harsh world of gang culture, violent ghetto life, police brutality and corruption to name, his brother and friends deride him as a coward, not to mention he's also dealing with the fact that his mother has been killed by rival gang members. His head is not in the right place, and he's at a very low, weak moment in life. So him acting like a lil' b*tch or softie at times was supposed to be the idea. As the game progresses, we see CJ's transition from young upstart street thug with very little heart and lacking smarts, to hardened, experienced original gangsta with more shrewdness, more brains to become owner of a vast, wealthy criminal empire - he was that classical underdog that was up against all odds in a long, hard struggle/fight, but came out a winner, on top. I thought that was a good idea and it was well written out, save a few caveats with the story (all that silly way-over-the-top Mike Toreno stuff and green goo etc). It would have been a bit boring and unoriginal if CJ was always a ruthless tough guy from the start that knew it all, and bulldozed his way to major success in the San Andreas criminal underworld - we saw all of that with Tommy Vercetti in Vice City, there was no reason to see it all again with CJ.
However I didn't like it when CJ was acting like a lil' b*tch with Catalina though, that part really annoyed me, and also the part when he was pleading with the cops in the boot of the police car. All of that whiny b*tch stuff in a very few small sections of the story did leave a bad stain on CJ's image, but for me it was so minimal I could overlook it, no one is perfect after all.
CJ was not the best GTA protagonist, but he certainly was by no means the worst - that honour goes to Trevor in my view.
Cesar being a protagonist would not have suitable for the core theme of SA, as much as you liked him. The black LA gang scene was much more well-known and infamous than Latino gangs at the time period that SA was based on (1990s). A Cesar-like Chicano character would suited V best, because of the current spotlight on vicious Mexican drug cartels.