If this is the case wouldn't it be make sense to allow (as an exception) these kind of transactions to be done by anyone (i.e. *without* signing) in order to reduce the number of UTXO, provided that:
This is not possible. Other nodes and miners do not (and should not!) know what UTXOs belong together. That would be a privacy breach. Also they cannot generate a new address for you to send it to.
The trivial case would be to combine UTXOs whose output scripts are 100% identical. These are all spendable by the same entity and this is publicly known information. This would even increase privacy in some cases, as fewer outputs available might leak less information about output selection algorithms by wallet software.
The Output scripts would remain untouched, it's more of a deduplication effort... a hardfork would make transactions legal that refer to identical UTXOs and combine them to a new UTXO that has the same script, but a combined value (no fee charged of course) of all inputs.