Why not Jack Broughton? It's impossible to say, but he might well have a chance if he spent a couple years adjusting under modern rules.
Any past champ given modern training tools could compete. Human evolution has not occurred in the last hundred years.
I'm always weary of getting too heavily drawn in to these 'old timer versus modern guys' debates (at least, that's what these kind of threads tend to descend in to), but the first all-time greats who I watch on film and think they display a style which would transition seamlessly in to any subsequent era are Tunney and Benny Leonard. That's not to say that guys who went before, such as 'Nonpareil', Jeffries, Barbados Walcott, Fitzsimmons, Gans etc. weren't all-time greats as well. They were. Moreover, it's not about evolution, more just education and honing. The late London Prize Ring Rules and early years of Queensberry were a seismic shift in pugilism and naturally it took a while for something passing as modern-looking boxing to spring from it on a consistent basis. For me, guys such as Tunney and Leonard are far more deserving of the title of 'Father of Modern Boxing' (or whatever people like to call it) than the likes of Corbett, who often has that honour bestowed on him. But that's just my take.
With how loose the modern definition of world champion has gotten. I suspect some early guys like Jem Belcher could make the transition well enough to pick up a title with good management, and a bit of luck. If you were talking aboutbeating Wlad or GGG under modern conditions, it'd be a very different answer though.
I cant think of any specific names, but I feel the further back you go, the much higher chance that a certain fighter winning a modern strap would have to be a brawler / extremely physically gifted, rather than a scientific boxer for a certain era. That's not to denigrate pioneers etc, as they were extremely creative, which all the greatest fighters should be. But they would have to be educated and adapted to modern rules and equipment before competing. The guys I'm talking about winning titles have advantages that transcend eras (power, size, chin etc). This is the reason why I'm much more likely to pick, say, Sullivan to win a title today than Jim Corbett (although Sullivan is definitely underrated skills wise). I would also pick Joe Gans, but maybe not 'as is', if he were plucked from a time machine and put into competition immediately. However, he would definitely adapt if given 6 months to a year, IMO, and dominate competition in his class.
All fighters would need short adjustment time, because they didn't fight under the same rules and conditions. With around half of a year and a few lighter fights, guys like: Bob Fitzsimmons Joe Gans Battling Nelson Would definitely dominate their divisions.
I'd turn this question around. How many or what percentage of today's modern champions (you tell me how many there are now) would have held a title belt in an era when there was only one champion in each division and when there were same-day weigh-ins?
I wouldn't pick Nelson. Just no where near skilled enough, really needed very long fights to wear down opponents. He wasn't really dominant in his own time either, Gans and McFarland were clearly better, Britt got the better of him in their series, only getting KOed because he fought a stupid fight, he lost to Wolgast, and some pretty mediocre guys. He was good, but not a style that'd make the transition well.