As far as I know no one on this thread has suggested that we must accept blindly any individual's evaluations of particular players, however distinguished that individual may be. That sounds like a straw man. For the record, I have disagreed with some of the assessments offered by players as great as Bradman and Sobers and writers as celebrated as Neville Cardus and E.W. Swanton. It is well known, for instance, that players often rank their own teammates higher than more dispassionate observers would.
An expert consensus is a very different matter indeed. If everyone or almost everyone who saw X and Y play agrees that X was a greater player than Y, and that X is one of the very greatest players of all time that information seems to me impossible to ignore. The expert consensus may, of course, be wrong, but I would be very careful about challenging it unless I had a good explanation for why so many observers got things so wrong.
My go-to example for this is usually Hobbs, since he is one of the three most universally admired players over the past century. Of the other two, very few really challenge Bradman's status, and I saw Sobers play many times, more than enough to make my own judgment. But Hobbs ... the stats may show that he scored 199 first class centuries at a highly respectable but not extraordinary average. But behind every stat there is a story. Hobbs's contemporaries stress that he only really exerted himself to amass runs when needed, that he was unequalled on a sticky wicket and that he could have scored a lot more runs if he had put his mind to it. These are things that do not show up in Stats Guru or its equivalents. And Hobbs is not the only player for whom the statistical record is not enough to explain his greatness. I could make similar claims about Dennis Lillee and both Barry and Viv Richards, to choose some other examples.
And what's the alternative? You Tube highlights? They are at best incomplete and even when available a very poor substitute. I agree that stats are indispensable for assessing players, but by themselves they are not nearly enough, especially when they are taken out of context. We need the backstory as well, and that tends to be found in match reports, players' memoirs and the like. It's difficult to take seriously any "analysis" that offers less.