Ime, as a parent if 14,10 and 7yo - yes I do occasionally feel a tiny bit sad when I look at younger pics that the tiny people are no longer here, but on a daily basis and overall I love who they are becoming just as much and I want them to have happy independent lives.
Honestly - be careful what you wish for. My 14yo has SEN and sometimes I wonder if he will ever be able to move out and be independent. Completely honestly I don't want him at home forever and though I absolutely love his little squishy self, I don't relish the thought of him as a adult living with me long term. He lovely (at times) but my job as a parent is to prepare and enable my children to become independent adults.
And the growing up happens so slowly and gradually, and brings so many new and unexpected joys, that for me I don't notice it unless I spend ages looking at baby pics really.
It's nothing like a breakup - that is unbelievably weird and as pp have said creepy as a perspective.