In light of recent events with Ledger, are all other hardware wallets susceptible to being able to export the private key as well, possibly with a firmware update?
Yes, including those that, like Ledger, use Secure Elements. Hardware wallets with SEs use the SE to store the private key, however in a way that can still be read from it by the MCU. Of course those that don't use a SE at all can also export private keys.
AFAIK, smartcards and yubikey are write-only for the secret, and can later only sign or decrypt data. Why don't they make hardware wallets in the same way?
Because that requires the SE to be able to perform the cryptographic operations necessary to produce valid signatures for Bitcoin. This requires supporting ECDSA, the Schnorr signature algorithm, and the secp256k1 curve.
While ECDSA is commonly supported, the secp256k1 curve is not. Additionally, Schnorr is not supported by any SE, particularly the specific variant that Bitcoin uses.