Corbett's resume is subpar at best, but some of his best performances have been in losing fights like against Fitzsimmons and Jeffries (past his prime nonetheless), and he managed to take Peter Jackson to a hard fought draw. Gene Tunney, after training and sparring with an old Corbett, claimed he had better defense than Benny Leonard. Corbett was clearly one of the best heavyweights of the 1880s and 1890s, so how much of a threat would you consider him in all time H2H matches?
Against the bigger guys from the 30s on? Not so much of one. Larry Holmes would have stopped him the way he did Lorenzo Zanon. Corbett too small for them.
Yes, a look at Corbett's record on its own does look thin. His better victories seem to be before he won the title - most noteworthy his fights with Choyinski and the draw with prime Peter Jackson. Upon winning the title he did what many other titleholders of his time and others did, made money from theatrical engagements and other non-boxing activities, in effect becoming a part-time fighter. He was doing well in his title defense against the older Fitz until he floored Bob in the 6th round. From then on, Corbett seemed to fade while Fitz grew stronger and ultimately KOd him with the solar plexus blow. Tom Sharkey gave him all he could handle in two fights with his swarming style, and he was only saved from a stoppage when his second entered the ring, resulting in a loss by DQ. Corbett did very well in his first fight with Jeffries and lasted until the tenth in the second despite being hurt early. When Nat Fleischer told Jack Johnson that he picked him as the number one all-time heavyweight, Johnson told him, "Why, thank you Nat. That's the nicest thing anybody ever told me. I've always considered Corbett the classiest boxer." Fleischer himself had seen Corbett box exhibitions and said that his boxing was showy. In the 1967 computerized heavyweight tournament, Corbett was matched with Jack Dempsey in the first round of the round robin. At least half of the experts polled picked Corbett to prevail, among them Jersey Joe Walcott and Fleischer. In the actual result, Dempsey won by a KO in 7. Like Gene Tunney after him, Corbett was a thinking man's fighter. He was always working on different techniques and experimenting with different styles. His relatively few fights and lack of film do not allow us to see the full range of his skills. In Peter Heller's book "In This Corner", Tommy Loughran tells of Corbett telling him after one of his fights that he enjoys coming to Loughran's fights. He enjoyed seeing him do things that Corbett used to dream about. Loughran asked what he meant, to which Corbett replied, "I only had 21(?) fights", while Loughran by that time had well over 100. I suspect that Corbett was better than his record would suggest. His skills were acknowledged and highly esteemed by those of his era. I have seen it suggested that Corbett might have given Johnson stiffer competition in 1910 than did Jeffries. Be that as it may, I would expect that Corbett would do well against slower moving heavyweights or those who did not possess a lot of power. He might be able to go into the later rounds with others but could quickly find himself in trouble with those who carried power into later rounds, as with Fitz and Jeffries. Fast starters with explosive power such as Dempsey and Tyson would be bad style matchups for him, as would swarmers with endurance like Marciano and Frazier, as evidenced by his Sharkey bouts. A Corbett-Tunney bout would have been interesting.
Not sure how he'd time machine travel from his own day; I suspect a Corbet-natural package, born into and actuating to the boxing game environment of other days in analogy to how he'd done in his own, would be a top contender with some chance to become a champion. 15/12 round limit might actually help him in many cases. Would love to see Foreman vs. a mid-70's Corbett.
His resume is a bit thin, as some have observed. However he seems to have been handily out boxing almost everybody, even when a late stoppage bailed him out. This might lead you to conclude that eh was better head to head, than his resume suggests. It might also lead you to conclude, that he could have done much better, with shorter fights and scoring that reflected cleverness more.
I’ll just say, for his day, while his record isn’t loaded with fights, he did fight most of the bigger names of his day - which included some excellent winning performances and some very good performances even when he lost - as the OP already highlighted. In a way, in view of his lack of total fights and his sporadic schedule/periods of inactivity, he perhaps could gain extra credit for the fights he did win and/or performed very well in even if he ultimately lost.
Giving him the benefit of the doubt I count 8 opponents over 180lbs in his 20 fight resume from which he gained 5 wins,1 over the shell of a nearly 5 years retired John L. Here are the known records of 4 more of his 180lbs + victims. Smith 1-1-0 McDonald 6-1-3 Miller 1-0-1 Kinney 0-0-0