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I am aware that the identity on elliptic curves is the infinity element.

Long shot (as it would be very useful to me): with that being said, does there exist a public key, pk, on secp256k1 such that, combine(pk, x) = x for all x?

combine is via (https://github.com/bitcoin-core/secp256k1/blob/cd470333351bd6d90296352f2a957f38bbdaf014/src/secp256k1.c#L725)

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As you pointed out, the identity is the point at infinity. It is also the only identity for addition over the elliptic curve.

But infinity is not a valid public key, for a number of reasons, and thus also not a valid input to combine.

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