It exists, it is called "UG", minimum capital 1€. You have to increase capital up to at least 25k though, out of your annual profits.
Second, not that I claim to be any representative, but this "UG is weird, unknown, not serious"... I have personally not heard that for about 10 years, so yeah, absolutely true when it was new.
Third, it's still relatively rare I'd say. You stumble over one every couple of months or years, in my experience mostly online shops without their own manufacturing (but maybe that is where I am looking) - if you just look at what tradespeople have on their vans: Nope, never. Always GmbH or GbR/single person.
But I have no insight into procurement departments.
People seeing a GmbH as more serious is just a cultural aspect, I’d say.