"They" don't want you to overbeat anything. Taken separately, overbeating the cheese would probably be a bigger problem than overbeating the eggs.
I don't know the answer to whether it's a good idea to beat the eggs separately, and incorporate them already beaten. In any case, they should not be added all at once though. The reason is to make sure they incorporate evenly.
It's easy not to "overbeat" when adding the eggs. Just add them one at a time with your mixer running at a low speed; waiting to add each successive egg for its predecessor to completely disappear in the mix. Once you've got them all in the bowl, finish fully incorporating them at medium low.
Overbeating cheesecake can be something like over-kneading biscuits or over-handling pie dough. That is, you can go too far in the direction of safety.
You're not going to overbeat at a speed low enough that it doesn't beat air in to the batter. If you want your cheesecake rich, creamy and silky, just don't beat too fast, and there won't be any problem.
Thus, there's probably not much benefit to mixing the eggs by hand, and adding them in several additions. But, what could it hurt?
Overbeating requires not just "too long," but also too fast. It's interesting that if you do overbeat, there are three likely consequences. One of which you might find attractive. That is, you may be willing to accept the resulting, lighter texture in return for the slight grainiess and greater likelihood of surface cracks during baking.
Sometimes I overbeat on purpose. Sometimes combining lighter, "fresh" cheeses (farmer, ricotta, "queso fesco," quark, etc) with creamcheese to make a lighter (and grainier) variation.
Indeed, there's a traditional Italian cheesecake called crostata ricotta which is all about getting that texture intentionally.
FWIW, crostata ricotta is a cheesecake in a pie crust. When I was catering (long, long ago), it was one of my primary dessert offerings and it got a lot of positive attention. It's an incredibly nice way of doing "cheese and fruit" for dessert. There's nothing better you can do to set off green grapes and vice versa. Siding it with fruit, further lightens the dessert.
I believe the recipe was posted fairly recently on CT, since I know petalsandcoco tried it with excellent effect. But, if you want to try it and can't find the recipe here, let me know.
Vee haff vays of zendink zee rezzipees,
BDL
