My understanding is that you can get rid of addresses and have people sign utxo's directly with ECC.
And having people share script (which contain condition to spend/lock the Bitcoin) instead?
It seems that addresses sorta function like accounts in eth and utxos's function for transactions in mimble wimble. Bitcoin seems to have both utxos and addresses and has some of the downsides of both approaches.
Wrong, bitcoin address basically is just abstraction/representative of script. It's also the reason you could send and receive Bitcoin using same address.