There are plenty of pros who do believe in the study of old games. Kobayashi Koichi, for example, puts an eloquent case for studying Honinbo Sansa in Fukui Masaaaki's book on Sansa and Nakamura Doseki. He rubbishes the idea of looking through the joseki prism and instead urges us to look at the qualities that brought players to the top (e.g. he highlights Sansa's tenacity). Fukui himself wryly illustrates how joseki ideas of even players as ancient as these, ideas once unthinkingly dismissed, have recently come back into fashion - Kobayashi too makes the point about openings being to do with fashion.
Against that, I have never been impressed by the way Japanese pros ritualistically and without explanation trot out the names of Dosaku and Shusaku as models to follow. To me this just PR all pros are taught to utter for the fans and doesn't amount to much more than the football coach's "it's a game of two halves".
In the end it is down to personal preference, but I have been struck by elements of this same debate in chess. In chess I think the debate is even stronger, because openings carry much greater weight and because there are many more strong countries where fans root for their own past champions. But what I've noticed is that even strong grandmasters tend to think modern players are clearly stronger until they themselves reach a certain point, such as becoming world champion themselves, and (perhaps because with their new eminence they are asked to write books with games of old masters, whom they now see with fresh eyes) they say they suddenly realise that some ancient was better than them all, or at least deserving of much more respect than generally accorded nowadays. I infer what is happening is that they have suddenly realised that top ancient players reached the top because they saw into the soul of chess in a way that only other top players can see. Kobayashi would fall into this category, of course, but few other pros could. This also squares with the wisdom of the ancients. Recall that the whimsical ancient name for a Meijin was
rushen (entering into the divine), which was an allusion to the Book of Changes, where it is explained as "When we minutely investigate the nature and reason of things till we have entered into the inscrutable and spirit-like in them, we attain to the largest practical application of them; when that application becomes the quickest and readiest, and all personal restfulness is secured, our virtue is thereby exalted." On that same basis, i.e. using the 9-dan to 1-dan titles of Emperor Xiao Yan's go academy, a mere journeyman pro is, depending on his actual grade 8- to 5-dan, merely "basking in the illumination" [of the Meijin], "has all the aspects" [but not the soul], "is well versed in the deep and remote" [but hasn't mastered them] or "is practising his knowledge".
By contrast we even lower grades (4- to 1-dan) "indulge in petty tricks", "fight with bodily strength", "act like fools" or "are content with being unskilful". Since this unnervingly accurate portrayal is from the 6th century, I'm not sure we can easily claim to have progressed much over the past 1500 years.
the classical players were notorious escapers.
This is almost totally false. It's true that certain players avoided playing certain opponents altogether, but almost all unfinished games known are quasi-ceremonial games at promotion parties, New Year parties, and the like. There were a few notorious
incidents (rather than players), such as Shusai doing this in China, but it was for political reasons and in fact he was known as the Fighting Mejin because he was the only 9-dan to put himself on the line and play in the original Oteai (giving handicaps, to boot). What did sometimes happen, though, was a kind of sandbagging: White might feel he had a big edge in a ceremonial game and, relying on his status, might decide to play it out.