10 years might be too short.
Much too short. There are a variety of very good reasons someone might not touch their bitcoins for more than a decade.
YOu are actually right. The correct timeframe could be more like 200 years.
I had been thinking about this issue and instead of creating a new thread, I decided to just add my proposal to the OP's since he and I have similar ideas. Hopefully satoshi if he is reading this would not only reward the OP but me as well.
Sweeping stale bitcoin utxos and putting them back into circulation
UTXOs older than a certain number of blocks are allowed to be mined by a miner and put into a block which will then delete the utxo and transfer a certain percentage of it's value to the miner that mined it. The other part will be distributed in a somewhat unpredictable/random fashion to some known active bitcoin addresses.
The UTXO set contains unspendable outputs. It also contains outputs that are theoretically spendable but can't be spent due to various reasons. Both of these problems could be resolved by adopting this practice of getting rid of stale utxos.