>why would the core project care how many times it's forked?
Some changes (eg. to the block reward schedule) are only possible on a hard fork as it makes the main chain incompatible with the pre-fork chain.
That's the philosophical difference between the projects: ETH is not afraid of hard forks and to this date, they have been uncontested. BTC never considers a hard fork and has had at least two major contested ones.
