The Jesus wrote...
I have to agree with biketough on this. He's also running around in a stereotypical Shinobi shozoku, albeit it a rather unique variation, but anyone who sees him will say, "Hey look, a ninja!" A real ninja wouldn't do something like that, a real ninja wouldn't be caught dead in a safety orange jumpsuit either, but that's beside the point. Ryu doesn't need to hide the fact that he's a ninja because no one he comes across will reveal his secret. When it comes to Ryu, you're either an ally or you're dead.
That is a pretty good reason for Ryu not to be stealthy, but just think how much more effecient he would be if he directed dome of his destructive powers into stealthy assasinations. I bet he could excecute at least eight members of a group of enemies, at once, before they even realize he's there.