Hi OP, this hit a note with me.
I've recently had to question this myself.
Both of my children {a boy and a girl} regularly get told how good looking they are, people say it to me and to them a lot, and I would judge it to be more than their peers.
However recently my daughter {who is 7} had surgery to remove a massive tumour in her chest. She now has a very big scar running around her trunk.
It has been heartbreaking after all she has been through, that her concern is that she is not going to be 'cute and adorable' {her words} any more.
Obviously from our POV that scar means the difference between her being dead or alive, so we are hugely grateful for the surgery. But she is the one that has to live with the effects to her body and self esteem.
We were able to have psychological support through the hospital, and one of the psychs questions was around why she values herself by the way that she looks, and places a big importance in that.
I'm sure there are other influences as well, such as TV, friends etc , but there is no doubt that these regular comments you refer to, have had a part in making her feel / value herself that way.
{FWIW, I've always made a point of telling both my son and daughter they are beautiful, for things that are NOT physically related, so that they do not associate being beautiful with their physical appearance.}
I DON'T think it's positive to ask others not to focus on it though, as I don't believe it is a negative. Just that it's not healthy to ONLY value yourself by your looks.
What we are doing instead for our daughter is focussing on her believing in her worth through other things, such as being strong, clever, determined and in relation to the scar, brave, given what she has been through.
We are also teaching her not to cover up the scar / how she looks {she is in year 3, so they still change for PE together in the classroom for example}, but to understand that her beauty is not defined by her physical looks, or the scar so she shouldn't be embarrassed for others to see. She wears a bikini still when swimming etc.
So I'd encourage you to do the same. IE not to make being good looking a negative thing / ask others not to focus on it. But instead to shift yours, and others you feel comfortable discussing it with, focus to other positive things instead for self worth. :)