Cards on top of eachother

Biggest concern that I see is the likelihood of cards becoming misaligned during the course of play. Just about every time that I've played a game with a table full of stacked cards, someone will bump it, and then we have to figure out which cards went where. A minority of people will also "accidentally" reposition cards.

quite easy to cheat with those

If you are talking about transparent "notches" and perfect alignment, I can think of two games that do this....Hecatomb and Gloom. Both games, at least at my house, require a constant eye on the order of the stacked cards so much that, at times, it distracts from the game itself. Whether it be cheaty players trying to alter the stacks for their benefit, a stiff breeze or my bastard cats - I can't keep my eye off an important stack for too long. Many of those concerns are apparent in typical games as well though more often seen in Hecatomb and Gloom - at least for me.

If this is a viable option, Forbidden Desert does a wonderful job like this with the water marker. It's a good idea to eliminate, at the very least the foibles of stiff breezes and dastardly cats.

Do you have a visual of the 3 overlaying cards? One of my old game ideas used two cards like so:

Rarely did the cards get bumped or moved enough to lose track of health.

Is this just a mechanic for tracking of "hit points" (or whatever you call them) or is there some other gameplay significance to it? Why three cards and not just two? If there is also a side benefit to taking damage, it could make for a fun game.

For instance, suppose the game were robot battles, and one set of cards represents your weapon and its power source. One weapon choice could be a cannon with a long barrel and a recharging piston that fires it. If you take one hit, the barrel is shortened, reducing your range and damage but increasing your attack spread, so you might hit more than one location for more total damage on a close target. If it is hit again, the recharging mechanism's controller is damaged, so you fire less often but when you do it is for even more damage (but with a chance of backfiring). Etc.

If it doesn't also fit into other aspects of the play, then I don't see the mechanism as being worth the problems that others have already pointed out. On the other hand, if its current state affects something else that you are using every turn, this actually ameliorates some of those problems, because it is easier for everyone to remember what state the cards were in after a table bump.