In the transaction's input a signature is a must. Otherwise, anyone with your public key (everyone, if you used your address before for spending coins) could make a transaction.
Agreed. That's why I wrote that the transaction should be signed with all public keys employed.
Second, UTXO (unspent transaction output) is a second half of the script that is attached to the input of the transaction that is spending those funds and needs to return 0 (maybe 1, I forgot) in order to be valid. So you kinda need it to make sure that you can spend the funds.
Does this mean the need to include UTXO is a concession to the powerful script system Bitcoin has? Put another way: in a hypothetical, very simple altcoin with no scripts and that can do only simple transfers, it would be possible to get rid of the need to include the UTXO in the transaction?