I've updated the text and the sample implementation to use this approach, it seems much better!
One reason we might not have thought of it, is that an idea had been to allow signet users to opt-in to reorgs by allowing a different challenge: ie, normally signet might be checked against "2 KEY_A KEY_B 2 CHECKMULTISIG" and the solution is "0 SIG_A SIG_B"; but if you were to use "DROP 1 KEY_A 1 CHECKMULTISIG" as your script, and KEY_A alone was used to sign short reorgs as well as the main chain, you'd be able to test how well your software handled reorgs, while people who used the normal signet challenge wouldn't see any of the reorgs. By actually constructing a tx to spend that includes the challenge, this doesn't work so well anymore.
On the other hand, it probably doesn't work anyway, because at the p2p layer, the peer doing the reorgs would try forwarding the to-be-reorged blocks to its peers, who would see them as consensus-invalid and ban the peer. So I think it's fine to drop this idea in favour of PSBT support.