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