I’m all for it. For any irreversible procedure there should be a 24 hour waiting period.
Tattoos are removable, with sufficient time, money, and pain.
Do you really want to encourage more government intrusion into private decisions, even stupid ones?
How about accepting a proposal of marriage? That's (hopefully) at least as hard to reverse as a tattoo. "Marry you? Gee, Honey, that's nice, I'll let you know in a day when the government thinks I've had enough time to think about it."
Buying a new car? The drop in value when you drive it away from the showroom is greater than what it costs to get a tat removed. Should the government prohibit buying a car for 24 hours after you close the deal? Is that any of their business?
Personally I think the government should stay the hell out of people's personal decisions, with very few exceptions. Making a stupid decision about a tattoo is small in the grand scheme of things.