WAR is a framework that can be developed in many different ways. Baseball-Reference and Fangraphs have the two that are best-known (bWAR and fWAR, respectively). If you want to object to it you can do so in two ways: you can object to the framework as such, or to a specific implementation of it.
If you are going to object to the framework as such you need to argue that there isn't a way to do what it's trying to do, namely, determine how many more wins a player would produce for a random team, beyond what a scrub from AAA could produce. I wouldn't recommend this kind of objection.
On the other hand, if you are concerned with specific implementations, the thing to do is to figure out what it is that B-R or Fangraphs (or whomever) does wrong.
Consider this. From 2010-2015 on average a team scored 0.481 runs from the start of an inning. If the lead off hitter singles, on average they scored 0.859 runs. (
Data from Fangraphs.) So the expected value of a zero-out single is 0.859-0.481 runs. (=0.378 runs) You do a similar calculation for one outs and two outs, runner on first, runner on second, etc., and every possible combination of those. Take the average, and you have the 2010-2015 "linear weight value" of a single. These values are the building-blocks of WAR. So Pete Rose gets credit for (3215 * linear weight value of a single) when calculating his WAR. (Although obviously you don't use 2010-2015 data for Rose.) So if you want to criticize a particular implementation of WAR you can argue that it's got the linear weights wrong - maybe something beyond the event (single, in this case), number of outs, and position of base runners, matters to how many wins a player would generate above a AAA scrub.
Or, Baseball-Reference assumes that a team of replacement players would have a .294 winning percentage (= about 47 wins over a 162 game season). You could argue that this is too high or too low. Replacement level players are the kind of guys who play in AAA, but sometimes get called up to the big leagues, but then get sent back down again. Not the top prospects in AAA, but the guys who are just a bit too good for the minor leagues but not quite good enough for the majors. You could criticize setting replacement level at .294 if you could show that these guys actually play at a level above that. Maybe if you took all of the last-guys-on-the-bench and made a team out of them they would win more than 47 games.
That's all fair game, although of course you need to have a reason for thinking that they've got something wrong. I happen to think that they do: whether a run is scored in the first inning or the ninth inning doesn't matter to the outcome of a game, but when calculating WAR for pitchers, we weight the ninth inning run more heavily (all else being equal) than the first inning run. That's something that we do when calculating WAR, and a reason to think that we shouldn't do it. So, if you think that there's something wrong with WAR: what's wrong with it? Answering this question will require digging through the formulas used to calculate it, but that's what's required to pose a serious objection to it. (And they're pretty interesting anyway.)
Last thing, on player comparisons:
Henderson and Mantle. Rickey had about 3400 more plate appearances than Mantle - a much longer career. That's what accounts for the difference. Their WAR totals are almost identical. If they had basically the same WAR, but Rickey's career was much longer, it means that Mantle was a much more talented player. WAR is a counting stat, so it's saying that Rickey produced more wins (above a AAA/25th man player) than Mantle did over the course of his career. But, for each game that they played, Mantle did more to help his team win than Rickey did.
Basically the same thing is going on with Yaz and Griffey. Yaz had more than 14000 plate appearances. About 3000 more than Griffey. That's, like, four extra seasons of full-time play. (Remember, Griffey got hurt a LOT.) Yaz has a lead of about 13 WAR over Griffey. 13/4=3.25. A player who produces 3 WAR in a season is above average, but not, like, a star. Since Yaz played the equivalent of four more seasons than Griffey, as long as you think that Yaz could produce at a level that's above average but not really a star, the difference between Yaz and Griffey is reasonable.
Niekro. Same deal. The man pitched 5400 innings. If you are any good at all and pitch 5400 innings you are going to win a lot of games for your teams. Gibson pitched only about 70% of the innings that Niekro did. But he has more than 90% of Niekro's WAR. What it's saying is that Gibson was a better pitcher than Niekro, but Niekro won more games for his teams because he pitched so many more innings. Ditto with Martinez. Ryan is a different story. He pitched almost exactly the same number of innings as Niekro. Now, Niekro really was slightly better at preventing runs from scoring (once we account for the parks that the two guys played in). And remember that, while Ryan struck out lots of guys, he also walked everybody and their brother. That makes a difference.