This problem has been referred to in "Utreexo: A dynamic accumulator for bitcoin state" by Tadge Dryja - #4 by lehnberg
The problem is resulted from:
Whenever a new block is mined, the UTXO set change, so ==> accumulator change, so ==> inclusion proof of every UTXO change. So the inclusion proof of every UTXO should be re-calculated whenever a new block is mined.
So user has to maintain full node to get the full UTXO sets, to calculate the accumulator and inclusion proof of his UTXO.
Or the user can request these data from “Bridge”.
But if there are millions of UTXO belonged to users connected to it, the bridge have to re-caculate millions times of inclusion proof, in every block interval.