Well a system that aims for security can not rely on self-asserted time, and there is no distributed secure time. If you start from a false assumption people will systematically abuse your assumption.
I know this as a principle, and also hard-won wisdom from real systems.
But, it's easier than ever before for a system to get a 'true' time, drawing it from the rest of the world: network services, radio signals, sunrise/sunset times. Though small numbers of systems can be faulted or frauded out of sync, systems for which this is economically important (like large mining combines) can get it right.
So though ugly in theory and provability, the assumption that most miners can consult and be rewarded to use an out-of-band 'true' time may work in practice. Or, may work as one of many informal hacks that deter sluggishness-for-profit.
Under the modification proposed, the miner can adjust self-asserted time in both directions, but his incentive is to report time as accurately as possible.
This is my intuition too. Since it is unpredictable when the miner's own next block, or a competitor's next block, will be found, there's no clear value other than 'now' (or maybe 'now+average_lag') to improve your block's tiebreaking power.
The same heuristic may also work with other timelike measures. As with Bytecoin's proposal, a miner could record when (by local time) they see each transaction. (A miner might even issue their own 'tick' transactions at regular intervals.) When receiving two competing blocks, they could prefer the one whose transaction-mix suggests a mining-time closest to receiving-time.