No it's not. Not all benefit is “income” and not all such income is universal. And it also has nothing to do with socialism (socialism is about forbidding the private property of the means of production! Please stop calling every kind of public intervention “socialism”, that's as ridiculous as calling all Republicans “fascists”).

For the non-income version see countries with free schools or free hospital, and for an example of an income benefit see the French Allocation familiales, which until 2015 were given to every family with 2 child or more no matter the parents income.

There were plenty of such systems, and some of them still exist (AFAIK the US social security is one of those, you don't lose access to the benefits even if you're rich)

Ok, those are valid examples (also, how about free roads for everyone? Everyone seems to take that for granted and wouldn't dream about calling it "socialist"), but in your original post you wrote about "a flat benefit for everyone" that doesn't reduce with income level, and the examples you gave are either non-income or not for everyone (e.g. not for families with less than two children, not for people who didn't pay social security taxes for at least 10 years etc.).