Guys with losses (not a rule but generally) guys who fought everybody, long careers and maybe it’s in how they fight that catches your eye. Toney is someone we acknowledge for this Canelo at one time? - Is it Crawford? I like Chisora and Parker for there grinding sort of fight everybody win some lose some resumes.
Completely random name. Edgar Sosa. Fought the who's who of the lower weights during the 2000's and 2010's. Krzysztof Wlodarczyk is another name. Still active even.
Unfortunately didn't debut after 2000 (he debuted in 1994) but besides that I would say he fits the rest of the categories that OP is looking for. I agree that the place to look is in the lower weights. I think basically everyone from the golden super flyweight era fits what the OP wants.
I'm talking about the likes of Roman Gonzalez, Juan Francisco Estrada, Wisaksil Wangek, Carlos Cuadras, Kazuto Ioka, etc
Pornsawan Porpramook had a short career but fought everyone offered to him in such short time too. Oleydong Sithsamercai fits this thread just fine. Omar Narvaez and Chocolatito might the cherry on top for the thread.
Can we run it back a bit so we can name Evander Holyfield? Doesn't get more classical than that. Even Muhammad Ali looked at matchups a bit toward the end to avoid fighting Norton again. I can't recall Holyfield or his team ever giving a single thought to matchmaking. He was a pure throwback. I know, this is obvious, but if we talk about fighters who would fight anybody without a worry about their record or how hard the match would be, he's got to be mentioned.