Not bad idea, but how to verify that someone is use/donate their time, computing power or mining hashrate while without makes nodes work too hard which could risk decentralization. Furthermore, how would the reward is calculated based on users time?
If you simply want to stop mining centralization, you could propose to change bitcoin mining algorithm with other algorithm which only can be mined with CPU/GPU (whether it has GPU advantage or not) which can reduce mining centralization.
Proof of Activity only combine Proof of Work (PoW) and Proof of Stake (PoS) which won't solve the problem OP mentioned if bitcoin still use algorithm which can be mined with ASIC.
If you simply want to stop mining centralization, you could propose to change bitcoin mining algorithm with other algorithm which only can be mined with CPU/GPU (whether it has GPU advantage or not) which can reduce mining centralization.
That is an interesting concept you came up with and I actually enjoy it and think it should be implemented. As far as I know there is something called Proof of Activity and Decred implements that on their blockchain but it isn't well recognized or it hasn't caught on yet. It seemingly is a similar thing to yours but I prefer POP over POA anyday 
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.Proof of Activity only combine Proof of Work (PoW) and Proof of Stake (PoS) which won't solve the problem OP mentioned if bitcoin still use algorithm which can be mined with ASIC.
so u mean if I want to implement this POP thing, the only option is to create a new coin???