Hundreds of years? My guy...how long do you think we've had unemployment insurance in place? Wtf are you even talking about?
This isn't complicated. I'm not even the one making the claim, it's the people who actually do "economics" that have been saying that the unemployment benefits haven't impacted labor participation. Even prior to benefits expiring in some states to give us relative comparisons, econ heads were saying that the benefits weren't the problem.
Can unemployment benefits reach a point where they discourage work? Of course...but that's not what's happening now and it's been looked at throughout this whole thing. I doubt you actually bother reading the articles, but this one cites more studies and explains how they come to their conclusions in simple enough terms that anyone can follow. I'll quote the conclusion...
Have Enhanced Unemployment Benefits Discouraged Work? | Econofact