If you can encourage spending - therefore wider distribution - instead of hoarding then yes, that would be interesting and a valuable feature. Perhaps demurrage (or negative PoS "earnings") on long held coins (like freicoin), combined with "Proof of time connected" to reward stable nodes and PoW for transaction processing.
Yes, one of the goals of such a hybrid design would be to encourage actual usage instead of pure speculation, but also better security, and even possibly price stability because with a more even distribution there could be less manipulation by large whales.
Demurrage is interesting and has already been discussed in some old threads about "stable coins", but the problem is that a "demurrage coin" would probably not have the level of acceptance a non-demurrage coin can have. Almost the same thing you can achieve with a slightly inflationary design (5% inflation instead of 5% demurrage), because people tend to ignore supply inflation (as in BTC and most other coins) but fear demurrage.
Nevertheless some years ago I proposed a combination of proof of stake with "locked deposits" (as in Decred) and demurrage: in this design you would get rewards when you lock your coins for some time and "stake" them, but be punished by demurrage if you hold coins without having your client participating in the network. That also could be an element of such an hybrid design.
Timekoin's "proof of time connected" is really interesting because it rewards stable nodes and punishes short-time involvement. It's difficult to implement in a Bitcoin-based coin, I know there was a discussion in Peercoin but it would have led to blockchain bloat because in each block, the connected peers would have been recorded, leading to very large blocks. In Timekoin the whole block processing process is different, that's probably why there this was not a problem, but I don't know the details of the implementation.
I'd also put a Proof of Service into it, what would reward real word services according to customer feedback and also could be a sort of escrow service.
I have already thought about a "Proof of service", but I doubt it would be possible, it almost certainly can be gamed by fake businesses and fake clients. NEM's Proof of Importance is the closest try I know, it calculates an "importance score" based on transactions and stake. So "hodling-only" accounts would achieve a lower score than typical accounts of crypto businesses (like exchanges, casinos or online wallets) that not only hold large amounts of coins but also move them.