Sounds like basically what a cryptocurrency hardware wallet does.
Several months ago I saw a project making wallet software that used the enclave. I forget who they were but I think they'll have a hard sell; everyone just reflexively assumed it was insecure because it was on a phone.
Indeed, cryptocurrency hardware wallets and the SEP are basically just HSMs (hardware security modules).
It's unfortunate people would draw negative connotations from it being on a mobile device. The security architecture of iOS and the SEP combined with the relatively wide deployment of iPhones makes for a great number of use cases.
The secure enclave uses secp256r1 while blockchain typically use secp256k1. Since private keys can't be imported, blockchain devs still require software interface until one or the others adopts the scheme.
https://www.trustedkey.com actually uses the Enclave and also the equivalent component (Secure Element) in Android phones.
Both of these modules use the secp256r1 curve at least, so the signature verification algo which runs on the blockchain can be the same for both types of devices.
(You can find some more details on this topic here:
http://blog.enuma.io/update/2016/11/01/a-tale-of-two-curves-...)
Since the Byzantium fork there are some precompiles available for curve operations. Using those for the r1 curve signature verification in EVM code brought down the gas cost to practical levels.
Ah, too bad. Ethereum is supposed to be adding signature abstraction, so you can use whatever signature scheme you want; maybe using secp256r1 with phones would be a good application of that.
