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While you do need "general purpose" computing for arbitrary programs, an ECDSA signature and checking some basic properties of a transaction like computing a hash or updating a database of records are small computations.
Big computation is stuff like "find an optimal path", small computation stuff is like "run a fixed algorithm over a fixed input".
I think generalized FE may be decades off.
But the use case for FE'd up covenants is using a small part of the FE power, so maybe much sooner!
Another way to look at it, is that FE should scale in the number of steps over and amount of confidential data. Applications that keep like a whole database or graph private are going to be expensive. Verifying a public computation and using a 256 bit ECDSA key are small.
Part of what makes it confusing is there are some definite bright lines to cross in terms of capabilities, whereby marginally more capability inside can lead to a way to stack FE blocks giving a more powerful FE block (e.g. building a CPU).