Is the current network difficulty algorithm appropriate for "Peak transaction-only mining"?
Interesting thought.

Years from now we may get to a point where transaction fees are the majority of mining income and profits are so marginalized that electricity expense is a major factor. What makes sense for a miner may be to have a low-power computer with ASICs sitting idle and waiting until there are some transactions with big juicy fees, then actually start mining. Once someone mined a block with those transactions the fees are no longer up for grabs, so your equipment goes dormant again to conserve electricity.

So far not a big issue I think, because the busy and slow periods are hard to predict. The problem is if we have certain times of day when a large portion of bitcoin users are asleep, resulting in very little value available from transaction fees. Or if you could artificially create a slow period by somehow hindering the propagation of transactions.

If you know beforehand that 50% of the hashpower will switch off for a certain time period then you don't need the infamous 51% hashpower majority to pull off a double-spend - the equivalent would now be 26% of global hashpower.

So yes, if a large portion of the hashpower switches off systematically at the same time, I think that could become a weakness. But I don't see it happening until we get to a point where most, if not all, of the income from mining comes from transaction fees.