For example on Casascius Coins, the private key is on a piece of paper that faces into the coin.  The hologram simply indicates that the paper hasn't been accessed.

You won't put private keys on the hologram, you would use them to cover a private key.

As it turns out, I actually do own a laser engraving machine.  But I am not lasering the holograms, the factory is.  I am pretty sure they laser the foil layer before it gets attached to the plastic layer of the sticker.  The foil presumably requires a much higher temperature to vaporize that the plastic would never withstand.  Where they mark at the factory, you see a complete absence of foil with no side effects to the plastic.

I have experimented with my machine... if I laser the stickers, I melt the plastic and create a sort of glittery effect as the plastic and the foil sort of melt together.  There is no feasible way for me to have any effect on the foil without having a much greater effect on the plastic.

My laser equipment is particularly handy for cutting pages of private keys into little circles that precisely fit the hollowed out portion of the coin that holds them.  But a good oversize hole punch would do the same thing (and worked for me before I got the laser machine).  I suppose with a hole punch, you play a guessing game on getting a perfect fit, where with the laser, I can cut any size I want.  (That is why, for example, I now put 30 characters in my coins instead of 22 - more precision means more usable printing room.)