It is a lot of work to get your name changed on every card, account, etc. Everything from bank accounts and any insurance policies to driver's licenses, passports and your library card. Now when you apply for a job and list, e.g., your references and degrees, you have to say "Oh, but they'd know me / the name on the diploma, etc. is Mary Jones, not Mary Smith." And so on.
Yes, you need a marriage license and that is an intrusive bit of bureaucracy, but because marriage remains a legal status change as well as a contractual matter between the parties, the license serves as sufficient documentation of, for example, the fact that you have become each other's legal next of kin. (Could all of this be done by a simple contract? In principle, yes; in practice, no.)
As for the supercilious observation that the woman is in all likelihood merely retaining some other male's surname, i.e., her father's, that's true but she didn't have a choice then, did she?
If women want to take their new spouse's surname for whatever reasons, most of which I'd probably disagree with personally, that's fine with me. My wife kept her surname back in the 70s when doing so was still very rare and we or she had to explain the decision too often to people whose damned business it was definitely not, plus stupid questions like "But what will you call the kids?" But if I had been the woman, I'd still have thought it less bother and less insulting than presumptively giving up my original family name.