Anything clothes related is linked to environment and context.
It wouldn’t make sense to wear a dress shirt at the beach, if you go running, at a rock concert, the gym, etc...
That should be 10% of the locations you’re going to hang out with girls (unless you do beach game).
If you are doing coffee shops, malls, street, etc... yes, it makes more sense to wear a shirt.
You could do a classy T-shirt too but most guys have their wardrobe filled with crappy T-shirts so a dress shirt is a much better staple unless you know about style.