Would it be possible to reduce the number of UTXO by making a transaction to self?

For example, if there are 30 payments to the same address A, this means there are 30 UTXO (assuming nothing was spent so far). If a transaction from A to A would be made (spending all BTC and sending all back to A), would this reduce the number of UTXO?

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:

(1) the amount is send from A to A
(2) no fees applied
(3) no other trx uses the respective UTXO
(4) number of UTXO is reduced

Sorry, if I completely miss how UTXO work, I am still learning.