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As I understand, p2pkh and p2sh are nothing better than p2wpkh and p2wsh, other than compatibilty.

After taproot, p2wpkh is also nothing better than p2tr, other than compatibilty(no economic incentive according to this).

However, when it comes to comparison between p2tr script spend and p2wsh, there would be an "economic incentive" to use p2wsh over p2tr.

If under following assumptions,

  1. Tapscript only contains "single" script(tap leaf is single).
  2. Script itself cannot be divided into multiple leaves(i.e. OP_IF A OP_ELSE B can be divided into 2 leaves).
  3. Script requires less than 5 signatures, as schnorr signature is more compact(about 6~8 bytes) compared to ecdsa DER format in size.
  4. No motivation to spend in p2tr key path.

All of the witness items to provide would be same for p2wsh and p2tr if locking script to spend is same, except that p2tr must provide tap control block of 33 bytes, even if it's only for single script spend.

However, I found the answer regarding comparison of p2wsh and p2tr here, which states,

As far as I can tell, P2TR is better than P2WSH in almost every way. I cannot think of a case in which it would be a significant advantage to use P2WSH over P2TR, except that P2WSH is already established.

Am I missing something? or is there other significant benefit which can offset this?

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Yes, having only a single leaf and all else being equal, a P2TR input costs 34 witness bytes (8.5 vbytes) more than a P2WSH input with the same script.

However, almost all current usage of P2WSH (which consists mainly of multisigs and Lightning channels) can benefit from the features of P2TR to reduce costs. Multisigs are cheaper with key aggregation schemes such as MuSig and FROST and can often use the key path to reduce costs even further. Lightning benefits from splitting conditions into multiple leaves, using the key path for simple key conditions and the aforementioned key aggregation.

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