It breaks some protocols, for example Proof of Burn. You can burn a coin in your coinbase transaction, just by taking less coins than you could. Then, there is no lost UTXO, everything is 100% clean, you just have some coinbase output that has lower uint64 value, and there are no other traces. But even if you have some OP_RETURN, then still, there is no reason to bring it back, because using OP_RETURN means that a particular user intentionally removed some coins from circulation.
Also, your proposal breaks some puzzles, for example this one:
https://bitcointalksearch.org/topic/reward-offered-for-hash-collisions-for-sha1-sha256-ripemd160-and-other-293382In that case, you would need to refresh those addresses every 10 years, just to say that "this puzzle is still not solved, but because of demurrage rules, it has to be recreated".
by simply logging on, opening the wallet
You cannot prove that you have access to some coin, without creating some kind of signature. You need to make a transaction, sign some coins without moving, or wrap some proof in some Homomorphic Encryption, but that way or another, "logging on" is not enough, you have to touch your private keys if you want to prove something. Also, you have to choose your accepted proof carefully, because there are ways to trick that you own something without having keys, for example in this way:
message="Hello World"
address="1psPJZYEJrjPtY6kw5Tqtj4mW2yXSSDuH"
signature="GwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAE="
Nobody has access to 1psPJZYEJrjPtY6kw5Tqtj4mW2yXSSDuH, but this signature is valid. So, if you want to accept some proofs, then choose them wisely, to avoid attacks like public key recovery.
A comprehensive analysis of the blockchain will be conducted to identify wallets that have not shown any activity for ten years. This process will be automated to ensure accuracy and efficiency.
If there will be some consensus rule, like "UTXOs not touched for 10 years can be claimed by miners, without signatures", then it will create a huge incentive to mine empty blocks. Currently, when the basic block reward will drop to zero, miners will need to encourage users to move their coins, because fees will be the only incentive. Your proposal breaks that assumption, because miners could collide, and say "let's mine empty blocks for 10 years, and then we will start collecting a lot of coins from the old times, before all of those halvings".
To ensure fairness and prevent concentration, the redistribution of dormant coins will be algorithmically divided among miners based on their proportional mining power, similar to the current mining reward distribution.
Note that "the current mining reward distribution" is "winner takes all". Of course, we have mining pools, but it is not a part of the consensus rules. Also, how do you want to compute "their proportional mining power", without writing all shares on-chain?
The entire process, from identifying dormant wallets to the redistribution mechanism, will be transparent and publicly auditable. Detailed reports and statistics will be made available to ensure transparency and build trust within the Bitcoin community.
I hope you don't want to introduce manual selection of outputs. That would be far worse than some simple, and automated rule, like "move UTXO without signatures, if age is greater than 10 years".
In general, demurrage is something that could be tried on some altcoins, or even better, on some test network. But doing that on Bitcoin would be a disaster. That way or another, if you think seriously about it, you should start from some testnet anyway (or maybe even signet, if you want to manually decide, which coin should be redistributed).
