It's possible, but there are two big weaknesses to your proposal over a multi-sig one.

Firstly, you are accepting far reduced security. If someone steals one share of your multi-sig, then they would still have a hurdle of 2¹²⁸ to overcome to brute force another share. In your system, if someone finds Vault 1 your security is reduced to 2⁶² bits, and if they find Vault 2 your security is reduced to 2⁶⁶ bits. (The difference being that 4 bits from word 12 are checksum). If someone steals Vault 3, then your security could be anything at all, depending on your passphrase. Unfortunately, few people choose strong and random passphrases, and instead pick passphrases like they pick passwords - short, predictable, and easily brute forced. You could potentially be down to a very low amount of security.

Secondly, you introduce a single point of failure. To spend from such a wallet, you need to bring the seed phrase and a passphrase together on a single device. If that device is compromised, then you lose everything. With multi-sig, your seed phrases can stay on separate devices, therefore protecting you against this vulnerability.

Obviously most people use single sig wallets perfectly safely, but if you are looking for the best security for long term cold storage or similar, then multi-sig remains the better choice here.