The use of the word "steal" remains improper. The coins subjected to this process of recycling would be the ones of "dead" wallets, i.e those wallets that have been inactive (no transaction) for a period equal to the full mining cycle (131 years). This same thing happens in nature. The universe doesn't steal energy from dead bodies, it recycles that energy channeling it back into the system. Bitcoin has a curious habit of mimicking nature when it comes to energy, except for recycling. Energy is never permanently lost in nature, it just transforms from one form to another. It seems that bitcoin neglects the recycle of lost money/energy back into the system.
So the first wallet balances to get recycled will be the genesis block and Satoshis'/early miners. At that point in time the block reward will have already reduced to zero, how do you propose to reset the block reward? You'll have a completely irregular supply of coins for the reward, you'll get a million or two BTC, and then after that you're not going to get big lumps and you might be able to track the possibility of any wallet reaching old age at a specific time, you can't be sure the owner won't move them and now you don't have new coins to hand out in block rewards. What kind of model is that for miners? By this point it is hoped that the transaction fees will be high enough to cover the cost of the miners, but you're going to release a bunch of "recycled" btc back out to them, do you know how that will effect the mining/transaction/user economy of the future? I don't.
I understand where the idea is coming from, but there are a myriad of factors you need to address to make this idea realistic or beneficial.