Cut and choose is required because there is no way to commit to releasing a private key.

You can commit to releasing the value of x such that hash(x) = y.

If both coins support CLTV, then you can commit to a hash and no cut and choose is required.

Few altcoins actually support it.  The cut and choose allows you to commit to releasing a private key for a given public key.  It's a cheat.

You commit to a hash of the private key.  The cut and choose is to make sure that the hash actually refers to a private key.

The other party can make an altcoin payment to a 2 of 2 multisig with confidence.  Since you committed to releasing the private key before the timeout, it eliminates the hold up risk.