What’s the logic in tasting and salting throughout? If you salt it to taste then it will end up getting too salty as it reduces, forcing you to top it up with more water (reducing the flavour from the meat). Why not just make the stock without salt, then use it to make something, and then taste and salt that other thing perfectly?
I don't know about that strategy in particular per se (though I'll spitball a rationale at the end if you're curious), but when making soup you generally want to split your salt between a conservative amount up-front and salting to taste at the end. Doing so
1. Ensures chunks of meat, veg, ... can absorb a little salt. Potatoes especially benefit from this.
2. Serves as a minor tenderizing agent for meat chunks (the effect is very small, you should pre-salt or pre-brine if you want it to be large).
3. Mildly dehydrates the other soup ingredients via osmosis, and prevents them from plumping up via osmosis the other direction when they have some internal salts. This concentrates flavors in the chunky bits and generally gives a bit nicer texture.
4. Gives you a smaller "gap" of remaining salt to add at the end. That's important because smaller quantities are easier for us to judge accurately, so you can get the salt level right in fewer iterations, and because a lot of people aren't methodical when taste-testing salt and accidentally saturate their taste buds if they have to try a few times (leading to an overly salty soup -- even to their own taste buds a few minutes later).
It has a few other minor effects. As always in cooking, those are just "changes" and not necessarily "positive changes" (and again, for most dishes the effects are small), but I usually like soups I pre-salt a bit better than ones I don't.
As to the actual technique you asked about, I think the biggest benefit would be an extension of point (4) above. Salting in small amounts with large gaps in time allows your taste buds time to recover and makes it easier to dial the salt in perfectly. If you frequently make stock you'll get a feel for what it "should" taste like at each stage, so the decreasing water volume will wind up mattering less than you might think.
Mind you, I don't personally like to salt my stocks. You have very different salt requirements for different end uses. If it's salty enough for a soup (which has tons of added water), it can't make a passable pan sauce (which has almost no extra volume comparatively). Adding the salt explicitly in each recipe is easier for me to work with personally. It also makes it easier to accommodate the occasional guest on a low sodium diet.
Tangentially, I often prefer to cook my stocks down into something like a demi-glace. They take less space in the fridge, they keep better, they're easier to use in pan sauces (where you don't want much extra water and need to be careful which stage you add the stock if you have to cook water out), they're no harder to use for soups (just add more water as desired), and I find them a bit easier to portion that way (if a recipe has specific texture expectations, you need to account for water percentage somehow, and having it all gone is an easy mechanism; even for other recipes, breaking off a chunk about the right size is fast, mess-free, and dishes-free, which is slightly less the case with liquid stocks). The biggest downside is just removing the hot water vapor from my home (old apartment, poor air-flow). I've been in kitchens where that's a non-issue, but at present demi-glace is a wintertime activity when I don't mind having a few doors open to pull fresh, cold air in.
Another tangential tip, roast the bones (250F for 6h, or 400F for 2) and meat scraps before turning them into stock. Most end uses benefit from the extra richness.
