I got married when I was 40. I kept my maiden name because I didn’t want the hassle of changing 22 years worth of legal/financial documents. I don’t mind when people call me Mrs. TheElf, though. I don’t bother to correct them unless it may make a difference in a business transaction or something.
My sister’s 3 girls have 2 different surnames, two carry her maiden name, one has her father’s surname. No one seems to care and they are still sisters. 
It’s really not that hard. Any couple that can raise a child together is equipped to manage a conversation about what said kids last name should be. With hubby and I, this took all of five minutes (we went Portuguese style). It’s not difficult, it’s not confusing, and there is no benefit whatsoever to a “standard” except that maybe guys whose ego is tied up in their last name are more likely to get their way.
And in some cultures, if a husband and wife share a last name, people assume they are committing incest!
I have never been in a position to have to provide proof that my child is mine at a moments notice, ever. I have trouble thinking of a single scenario when I would need to prove they are my kids that couldn’t be anticipated and the proper documentation provided.
My kids are listed on my health insurance cards when they’ve gone to the doctor or ER.
I brought their birth certs to register them for school.
I’m listed as parent/guardian on camp/school etc forms and simply show ID, if needed.
Under what circumstances would this be necessary?
In Quebec, women are not legally permitted to change from their maiden name. They get to choose their children’s names (possibly hyphenated), but once chosen it can be changed only by formal court order.
I know a woman who has the same name as her husband (they are actually cousins). Her employer could not issue pay checks after that law was enacted since the employer changed his software to require that the maiden name differ from the spouse’s name. They just gave her spouse a slightly different name.
Immigration official at airports for one.
That would be a “planned for” example. Of course I’d have their passports, birth certificates and any custody agreements (if relevant) in hand.
I’m talking about being stopped unexpectedly and getting challenged about my legal relationship to my kids, such that having a government issued card I should carry would make any sense.
I, myself, will not be changing my name after the OP’s divorce
(no, I won’t “Think of the Children!!!”).