Is it rare for a high baritone to sing tenor?

Hello everyone, I'm glad that I've finally expanded up my range. It about 3 octaves . From E2 to E5 sometimes F5. My chest could go up to A#4. But however what keeps worrying me now is that people kept saying that baritone mustn't sing tenor range. As for me, I could reach up to High C but mostly in my mix register without force. My timbre are slightly darker and less piercing though. More round I'd say. Hmmm...I can do falsetto but not pretty good(lack of control) unless if it's above my range. And the max I could go with falsetto would be B5. Just wondering why some other males could sing above C6? Thanks in advance :)