No, because each input's signature commits to the entire context of the transaction. If signatures attached to any input that spends from the same output script, you could replay transactions to spend other UTXOs that share the same output script.

The signature is bound to the UTXO, so it's different for different UTXOs.

It's not the same for all UTXOs - but for different reasons between signatures and hashes.

Signatures have a property called "binding" - it means the signature and what you signed are bound - the signature is a different one when you sign something else.

Hashes have properties called PR and 2PR - it means for a given hash it's impossible to find any preimage.

Another thing I just remembered: Since Segwit this isn't relevant anymore anyways. You gain nothing by making the witness smaller

Also also because maybe you find that interesting: There is a cryptography called "aggregated signatures" which lets you save multiple signatures in the same amount of space as only one signature. It works with the Schnorr Signaturescheme