Name the one most important factor that would make this scenario
implausible (say, hominids before this or that era were physically
unable to speak), or if you prefer, more plausible (for instance the
larger brains of Neanderthals).
Scientifically, the most implausible thing about this is contained in this statement: "Tens of thousands of years later, a different branch of hominids attains sapience, and the cycle repeats." The problem is that if you look at the Earth and the human race today, you will notice that there are no other hominids left.
That's almost certainly because we out-competed them (whether intentional or not). And there's no reason to think that whatever hominid won the arms-race the first time wouldn't have done the same thing, leaving no remaining hominids for us or any other "pulse" to evolve from. However, that's a scientific detail that the general public is almost entirely unaware of, so from a story/fiction standpoint, it might not be a big problem.
Do you think (m)any XXI-th century level artefacts could be preserved
well enough to be detectable from 30-50k ago (especially given the
dramatic changes in sea-shore levels in the past 50k)
Sure, just not the ones from the shores. If you look at humans today, we have virtually covered the planet to such an extent that I would say that the only way that a succeeding intelligent species would not be aware of us is if we went to great effort and expense to cover ourselves up from them. Really, we would have to scour the whole planet to have a good chance of preventing them from discovering our history.
One possible way around this might be to invoke some specialized technological disaster like a nanobot war that disassembled/disintegrated all humans and their technology. Personally, I don't think that's feasible, but lots of people do think that it is.
What would the one most important result of this type of 'pulsar'
intelligence be in terms of pulse-driven changes across different
intelligence bursts? I'm thinking for instance that the next
post-human pulse for instance would have a lot less coal and oil.
Perhaps they trigger (the end?) of an ice-age, or genetically modify
their successor race before they leave.
Well, the energy thing is huge (and one of the best ways that we can be certain that their wasn't another intelligent species only 30-50,000 years ago). Discovering so much free energy lying around, easily accessible and exploitable has been a remarkable stroke of good fortune for us, akin to having our whole species win the Lotto. And now that we've used up so much of the easy/cheap stuff, any species becoming sapient after us will have a much tougher time of it.
Other non-trivial persistent changes that we are making:
Massive Climate Change:; melting most of the glaciers & ice caps. Though this could recover on its own in a few thousand years.
Space Debris: The low-orbit satellites will degrade and fall back to earth eventually. But the stuff in high-orbit (includes all geo-synchronous satellites) will likely still be there. Also, the Apollo landings and the stuff we left on Mars, could be discovered.
Radioactive Materials: It's not just oil and coal, we're using up most of the easily usable radioactive ores as well.
Species Extinction: We didn't stop with the Hominids, we are still killing off species at a faster rate than anytime in the last 60 million years.
Mineral Redistribution: Most of the worlds surface gold, silver, diamonds, etc. are no longer where nature put them. Instead they're either spread out across the whole world (like the rings and other jewelry so many people where), or else concentrated in huge concrete and steel vaults (like Fort Knox). Neither will make any sense to future geologists.
Sooooo Much Garbage!: We make a lot of it. Really an incredible amount. We try to bury, sink and hide it, and much of it will decay, but still, incredible barge loads of it will survive. And our successors will find these stunning huge landfills and dumps of unbelievable amounts of plastic, toxic chemicals and other slowly rotting stuff.
Really, I could go on and on here ...