Absolutely.
You change “status” in the eyes of some. Coffee, cup of tea , or lunch (often “ladies”) if you are lucky, at best.
My friend in Scotland lost her husband while in her 50’s and made the same point as OP. Oh no, I said, that is because where you live is still in the “Dark Ages” with formal dinner parties - that wouldn’t happen down here . Huh!
Well it does- anywhere.
As a woman on her own (I hate the term widow) one might enjoy coffee with a friend, or if lucky, an invitation to lunch with a couple. The best friends for me were the sensitive ones who invited a few others as well, so that I didn’t feel I was creating an odd number.
And before anybody says why don’t you do the inviting, I do, but admit it is always lunch, especially in summer in the garden, not least because doing the meal, drinks, plus the hostess chitchat is hard work for one.
Ro60 makes a good point too - and I hesitated to make too much of it as it sounds self-pitying, but yes, you drop off the radar.
Like Scribbles says, sometimes you have to pluck up the courage to invite yourself, but the fear of rejection is that much greater when alone is the default position.