I don't know about "damage to machine" but perhaps "to wallet". Certainly, if it takes a user 10 or 15 or 30 (!!) Clean-Printhead Cycles, then wallet alone isn't just a factor - it's all that wasted time of sitting there, every minute or two, running another cleaning, and another test print, then starting all over.
Do that for an hour, and it's pretty torturous. Ask someone to do it over 2 hours, and they'll find other things to do. "Sorry - I had to poke my eye out with a sharp stick... I'll try again tomorrow, OK?"
That was actually more of a concern - wasted time - than the final cartridge costs - which could be exorbitant, too.
But I don't know about actual physical damage. IF that occurs, I'd march the unit back to the RMA process and use overheated-print circuitry as my complaint.
Our Epson Artisan & Expression 'fails' were all involving the Black Ink, and those appeared just after the Half-Usage Level on the ink cartridge. By that point, the print-head was clogged and couldn't be cleaned with THAT cartridge.
One successful experiment was to install only a Genuine Black, do the print-head cleaning, then replace it with the Clone Black and proceed. That worked for about the same amount of time - another "half of Black used" before clogging (streaks, stripes, blobs).
Cleaning the print-head once a week or every few hundred print jobs isn't a bad thing, I'd suspect.
So an argument might be made to "use Clones, and do cleanings twice as often, saving the expensive Genuine for that purpose alone."