This is a very valid point, OP.
I separated from my husband when my children were 13 and 6. I knew a couple of women who were parents from my daughters dance class. We didn't know each other well but occasionally met up for coffee/lunch. After I'd been separated for about 6 months, I went for coffee with one who told me that, when I'd told them I'd become separated, they felt sorry for me and were worried for me. But, 6 months later, they were both a bit envious of how happy I was, how I was talking about going out, having hobbies, weekends away and seeing friends. She laughed and said she might try it.
Yes, it was a flippant comment but the point is that relationships and marriage aren't always all they're cracked up to be. Yes, it is lonely and God, can it be lonely! I remember well the aching black mass of loneliness that I carried with me everywhere for a while. But no one else saw that. They just saw strength, freedom and opportunity. Just as I only saw their companionship, togetherness and having got it sortedness. I didn't see their loneliness or sadness either.
I also agree with the poster who said some of it is about 'reframing' to yourself.
Some of those other parents will admire and envy you for your strength and independence. Some will wonder what you've got that they haven't to not need someone. Some will feel pathetic for putting up with their crap relationship when they could have what you have. Some will hold you in mind when planning to leave at some point.
What actually helped me the most was joining a choir. Sounds daft but there were a lot of people 5-15+ years older than me (I was 37). They either had no childen or older children and were no longer spending weekends doing 'family stuff' and many of them had divorced themselves or were long time single - male and female. It was really liberating not being the only single parent in a room full of parent couples and just being in group of independent people who were just doing things for themselves with a range of life experiences and relationship experiences that had led them to where they were. I was just one more person with one more variation on a theme life story. We did holidays, youth hostelling, gigs, theatre trips, nights in the pub, house parties... Great times.
I'm not recommending you join a choir (although it was good fun) but advocating for getting out there and meeting people in different circumstances so that you don't always have that feeling of 'always being the lone person showing up'.
Eventually, being single feels less of a burden you carry and more of a superpower tbh.
I'm in a relationship now. I eventually met someone through one of my hobbies. But I always know I'd be ok if I became single again.