Is it possible to add solona style timekeeping in the blockchain to improve tps/settlement time

Solona's way of solving part of the scalability issues of scale 1 blockchains is having each validator keep its own time. This seems like an easy thing to integrate into another blockchain, but many hav'nt? Would it be difficult to do so?

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I find that sharding is still not going to alleviate the concerns with quick transactions that can be used by say credit card companies or decentralized order book style exchanges.

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What are the drawbacks to solona's timekeeping method? It seems very smart to use essentially the same technique to get effectively increase bandwidth through the network as cell phone towers.