It sounds plausible, I’m a bit stuck on the a holder is a holder no matter where they are self custody or third party
I disagree. Those who don't own bitcoin cannot be called holders. Keep in mind that if you buy an ETF or basically even when you buy bitcoin through a middle man who ends up controlling your coins, you DO NOT own bitcoin. You are just investing with that third party.
So are they going to decrease on-chain transactions?
I don't think so because I believe at the end of the day the number of people who invest with third parties in the name of bitcoin is going to remain lower than number of people who actually buy bitcoin themselves.