No matter what you do, this will cost server infra. That's Musk's argument for disabling access altogether.
Therefore it would make sense to have a solution which burdens the client disproportionately in relation to the server. A burden so low for the casual user that it's negligible but in aggregate, at scale, would break things. Which is what he wants.
Looks to me like both reddit and twitter are using the wedge to rather increase the height of the wall of their gardens and kill 3rd party development as opposed to genuinely trying to license bulk-users appropriately.
You're gonna need to license api keys so you're already identifying consumers and there's your infra which you need anyway. At which point you can throttle anyone obviously abusing whatever free/open-source tier offering you give out as standard.