You seem to be assuming that people invested in ETFs are all morons. Large corps and insurance funds would not benefit from printing, and it is almost costless to verify and require that information. It's much more profitable to move the price in desired direction once you have significant share of the marke and enough fiat for leverage, and not risk your customers turning on you.
Discussion
I'm not talking about ETFs, very few people will care about them in a couple of years anyway.
Not specifically ETFs anyway. There's practically infinite demand to print Bitcoin for free, the bankers will make it happen one way or another. The only thing that can stop them is demand for real (self custodial) bitcoin.