It depends on the nickname, I guess. So far my villagers only suggested nicknames I didn't like.
What I really dislike is when villagers want to give you a nickname with only the first letter in your name, like "Fancy T", "Doctor F" or whatever. I think it makes no sense to call someone by only their first letter.
I've never really gotten a cute name from my villagers, except for when I had my first villager Merengue back in 2014. She called me shortcake. Otherwise I haven't gotten many good nicknames, but I still tell them it's fine they call me whatever they want, because I really don't have the heart to turn my villagers down. ;-;
There are some nicknames, which I don't like and where I wish that I said no to them, it's kinda a fail
when you didn't pay enough attention when a villager suggests you a nickname, you still press B and
then realized later, that they gave you a silly nickname you don't wanted. And then every villager ask
you if they can use the nickname too. I prefer more the costum nicknames, because at least you can
control it and choose on your own how the villager should call you.
I don't mind the nicknames. I usually think that they are cute and add more individuality to the game. However, if they suggest something that I detest, I decline the nickname. Right now, there is a trend among my villagers to refer to me as sweetums.