Hall voters don't vote for every player in history. I don't imagine many players from the 1920's are currently up for Hall vote. I'm no expert on precisely each individual voting, but certainly they've watched the guys from the past couple decades who are the ones, by vast majority, coming up for election. If I'm wrong there let me know, but I'm pretty sure I'm not.
I was playing with some hyperbole when I said they see as much of the players they vote for as year-by-year awards, but it certainly isn't far off and would be subject to a case-by-case basis anyhow. There is always major concern among fans and some voters of all the sports leagues, including the college levels, that many voters simply don't have the necessary knowledge to vote on the awards. In other words, many of them aren't watching the amount of games they should and so forth. To be frank, I don't trust the people voting for the Hall or the awards at all, especially when it comes to writers voting. Sports writers are among the most biased people imaginable.
It is a very good question how they measure players from one era and another. The simple answer is that they all use their own criteria and that is for the best. You'd think that then collectively the results are pretty good. Sure, your system shows different results than the Hall voters. Well, for starters there have been many different Hall voters through time. It would be down-right frightening if you were able to come up with the same list that many different people through many many years came up with. However, that means you found the Hall of Fame to have a different measure of greatness than your system. It doesn't mean it isn't a measure of greatness any less than yours. Because who says yours is perfect? Perhaps you think it is, but then you have a bunch of people who disagree, thinking yours isn't a measure of greatness.
That's just it, we aren't supposed to agree. To say though that the Hall isn't a place for the greatest players of all-time simply isn't fair to those who are in it. It may not be a place for every single great and it may be a place for some not-so-greats, but it does a good job all things considered. It is the only Hall of Fame we have (well, there's the international one). Part of the fun is arguing who we think should and shouldn't make it. Saying "well, here is a list of exactly who should and shouldn't make it according to some strict statistical criteria, nothing else considered" isn't very fun. However, saying "well this and that, blah blah, plus he finished 20th in my system's list and all the other guys in the top 25 are already in the Hall" takes your system and makes its output relevant and interesting... without being so absolute about it.