NOOOO
Only BA have the silly limit and to be honest, there are far more opportunities than just BA.
Don't worry about it. I'm in the mid 6' and fly biz jets and it's not an issue for me so if you're looking to get into the larger airliners, there will be no problem.
It's BA's post airforce mentality that's led to their limit, but it's not like you'll be ejecting from a 747.