My mum is late 70s, I'm mid 40s and she has moved city but still travels back twice a month to the city I grew up in to see the friends she made at the school gates.
I have a lot of amazing friends from the school, I never understand people who say "all you have are kids in common..." as we are a similar age, life stage, we have chosen to live in the same area in the same city as each other (an area where you are choosing vibrancy and culture over affording a bigger house). That's more than I have in common with some of my oldest friends.
I think it's really important, we help each other with childcare, we talk through things that our kids might struggle with and now my DD is at high school we msg each other when the gang of girls have gone back to someone's house and we might wonder where they are. I genuinely care about their kids and they care about mine. I also have friends I've made, where our kids don't get on particularly well - they are brilliant and its great having local people you know, bumping into people etc.
On a smaller level, the kids benefit because if there is something fun happening locally, I'm more likely to have someone tell me and there will be people they know there. We share lifts to activities, so they can do more things. We ask what gifts they would like and can swap books etc around. My shy, ASD DD has definitely been invited to more parties than she would have been if I wasn't friendly with the parents.
There is nothing to lose, don't look for reasons not to try and make friends - scout out the people you think you'd like to know - life can only be the richer for it!