I have zero problems with playing a paladin with a code of conduct. Nor, do I think, does anyone have any problem with a paladin having a code.
The problem comes with the idea that the DM is the one who should be the final arbiter on the code.
I mean, heck, Mournblade has flat out stated that if I play one kind of paladin, I can kill things that detect as evil on the spot. You state that doing so will cost me my status. Who's right? Prove it.
That, in a nutshell is the problem with leaving it to the DM. If I play a fighter in your group or in Mournblade's group, my character could be pretty much exactly the same and there would be no problems. But, I cannot play the same paladin in your group as his group. Not because you are using different rules. You are both looking at exactly the same rules yet giving completely opposite rulings.
And you see no problem with this?