Here's my argument for a pretty face young Batman:
I think it creates an interesting contrast between his Bruce Wayne persona
Sure, maybe if we were talking Batman in his mid 40s, mid 30s, late 30s, etc. he'd obviously need to look rugged and serious and imposing, but that's partly because Bruce Wayne (the public persona) obviously has to mature as well.
here, we are talking about a young Batman, one that's just starting out.
25-35 year old Bruce Wayne. Without the cowl, he looks handsome but he doesn't look like a guy that'd fit pretty well and by his mere look impose in a harsh war setting like idk, Jon Hamm does (to put an example), he looks like what he's just supposed to be for the public: a young, non caring playboy that looks like he'd fit well in any given random party of young attractive rich entitled adults that'd make for the cover of some crappy tabloid site or belong in a show like Gossip Girl or Glee.
Which is why what he considers to be his true self isn't represented not even in his face what the public sees, or what the girls he dates see, it's instead reresented by the moment he is behind the mask, all his pretty and non threatening features covered by a dark mask with some demonic qualities to it, that allows nothing to see except his jaw and his eyes that in those moments express nothing but anger, frustration and just a general feel of discontent with the world surroundig him. His true self is also shown when he's underneath the cave, his face covered in some very small shades of lightning, weary, with an stressed focused expression.
When he's finishing taking a shower and looks himself in the mirror and practices a smile to keep practicing the acting of his Bruce Wayne persona, when he looks at that pretty face and pretty smile, he doesn't see himself. He doesn't feel identified with the man he is seeing in the mirror, with the face he's been born with it, instead he feels identified with the reflection that he gets to see of himself when he looks over a dark screen in the Batcave, and he sees the same monster in dark clothes that th criminals see, and he takes off the mask to see a low res glimpse of his face, but now weary, bruised and with the look of a broken, depressed and mysterious man.