Are there any reasons this TapScript would be better
Taproot always allow you to spend coins by key, or by TapScript. If you provide a valid key, then you can always skip the whole TapScript, whatever it is.
than simply storing two Keys in the bunker from a 2 out of 3 multisig?
It is more expensive to use 2-of-3 multisig, if you can spend everything by a single signature. Just compare it:
Size: 204 bytes, Transaction:
https://mempool.space/signet/tx/3e23b16739a909d69f536bed7738a0618af8b8ccdab32f7cebeab77111a66ac7Size: 420 bytes, Transaction:
https://mempool.space/signet/tx/a037170f1d35666c070a4f04138f1d9c34c64a8d86514e4254e75571997a575aOf course, you can always push 420 bytes, instead of 204 bytes, but it is up to you. For bigger multisigs, spending by key is cheaper, than touching TapScript.
And even if you use P2WSH, demonstrated by ercewubam, then still:
Size: 315 bytes, Transaction:
https://mempool.space/signet/tx/1f44edd2663a0b7492f092cd83a41aa4083462837066cdffde31da9e19302ed2Size: 375 bytes, Transaction:
https://mempool.space/signet/tx/b7b08e914cc7112d533b4e6c690ba1997c735cfafb83293d19aa838481ed3dd7So, as you can see, multisig takes more bytes, when keys and signatures are explicitly pushed to the stack. It is up to you, if you want to pay more for your transaction or not. Also, Taproot has an additional benefit, that if only bunker is used, then nobody knows, that there is any 2-of-3 multisig at all, if it is never revealed (in P2WSH, the whole Script is always pushed, even if a single signature makes it cheaper).
