At face value, you're right. His mark is pointless, and in the colosseum case, degrading even.

But a lot of ancient buildings are nowadays studied for the marks found on them. If you squint your mind's eye a bit, you can even imagine that some of the cave paintings that we nowadays admire are nothing but a testament to some dude's wish to leave their mark. No one cared until someone started to care.

Funny how relative all these things are, right?