Could RSA keypairs be used for cryptocurrency addresses?
You could do this, but you'd have to replace 32-byte public keys by 256-byte public keys and 64-byte signatures by >=256-byte signatures in the storage format, assuming you used 2048-bit RSA moduli.  There are techniques for compressing RSA signatures, but I've never heard of anyone implementing them, so you might be on your own to write the code, and they won't beat 32-byte keys and 64-byte signatures at a remotely comparable security level.  And, unlike ECDSA, RSA key generation is sloooooooooooooooooow.

Alternatively, you could use a Schnorr-style signature scheme, such as Ed25519, with size and computational cost comparable to the ECDSA over secp256k1 as used by Bitcoin, and then reuse the key pairs for ECDH/ECIES, like XEdDSA does.  There is no shortage of ways to shoot yourself in the foot designing and implementing a bespoke cryptosystem, but the combination of EC-Schnorr and ECDH with the same key pairs does not necessarily seem to hurt security in itself.

(Whether you can do this with ECDSA, I leave this as an exercise for the reader to study.  I'm not aware of literature on it; if you find any, please answer fgrieu's question on the subject!  But your time is probably better spent just using XEd25519 than fussing with ECDSA.)