1. Coins haven't been spent doesn't mean it's lost (even though some of them are), maybe the owner simply hold the bitcoin for long-term investment.
2. Why would we eliminate satoshi's stats or force satoshi to move the bitcoin? It's contradiction with bitcoin goal.
3. It would take some computational power just to find unspent coins and add it for future circulation
4. I don't see the connection between unspent coins become mined after few years and limiting block size/allowing much more tx/second.
5. I don't think it's good scaling idea since your idea require more computational power and more time to develop/test the idea without much result. Even change max bitcoin supply or add "annual return" feature is slightly better idea.
CMIIW.
1. I don't see a big deal to move all your coins once in 5-6 years.
2. Agree. But if he has private key he can just move it. Of course this way everyone will be able to deduce some information about his activity but it's not like people don't expect him to return at some point. Just a little bit of certainty.
3. It should be done only once - at certain block height block header will contain information about all aeged coins.
4. Let's say coins can be spent only if their age less than 700 000 blocks. This means that after block #700 000 all previous blocks become irrelevant. This means we will always have hard cap of blockchain size. We can limit it without fear it will grow out of control. We can say "Blockchain can never be more than 1 TB (this isn't that much tbh)" and make blocksize bigger without fear of centralization (scenario where normal users wouldn't be able to host full node because they ran out of available HDD space)
5. It won't take more computing power. Miners will only need to check if coins that are being spent in tx are younger than certain age. It won't affect POW at all and POW is what consumes computational resources.