No it doesn't it's the other way around.
I'm not calculating market cap. I'm calculating the max value of a fixed coin asset, not the current.
If their scarcity is the same then their value per share(token) should be the same.
Therefore the token price multiplied by the max number of tokens should be the same.
I'm ignoring the other metrics like utility and decentralization which most certainly will have effect.
Lol scarcity being the same does not imply value is the same, that only holds with equal utility.
Anyway read this from 2017 if you're interested in a well-argued case about relative max valuations of store of value vs utility tokens:
https://s3.eu-west-2.amazonaws.com/john-pfeffer/An+Investor%27s+Take+on+Cryptoassets+v6.pdfThanks it's going to be a good read.
Yes an asset is more than its scarcity. For Eth going from not-scarce to scarse should have a positive effect regardless...