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Spaceflight Now's U.S. military tracking unguided re-entry of large Chinese rocket includes the following:

In the case of the Long March 5B, the core stage delivered its payload — a prototype Chinese crew capsule — into a low-altitude orbit. The heavy-lift Long March 5B is designed to directly inject payloads into low Earth orbit without an upper stage, meaning the core stage also ends up in orbit, instead of immediately falling back to Earth in a predetermined downrange drop zone.

  1. Would this then be regarded as a single-stage-to-orbit, and a survivor of astronaut Don Petit's tyranny?
  2. Are core stages going to start falling unpredictably from orbit† somewhat regularly now?

†as opposed to falling a long distance but somewhat predictably down range into the ocean as planned, or landing on a boat††.

††yes it's a ship not a "boat", looking for the original video where Musk made this clear in a press conference.

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    $\begingroup$ It's not SSTO unless shuttle was. It has 4 strapon boosters that get jettisoned. $\endgroup$
    – Organic Marble
    Commented May 10, 2020 at 4:39
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    $\begingroup$ Looks like your intuition was good. arstechnica.com/science/2020/05/… $\endgroup$
    – Organic Marble
    Commented May 12, 2020 at 22:37
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    $\begingroup$ @OrganicMarble yikes! $\endgroup$
    – uhoh
    Commented May 12, 2020 at 22:41
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    $\begingroup$ I think this also caught them off guard. I wonder what their long term solution could be. BTW what's the space shutter and buran's plan for this? Does their tanks also circle the earth multiple orbits and reenter uncontrolled? $\endgroup$
    – user3528438
    Commented May 15, 2020 at 19:19
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    $\begingroup$ @user3528438 Space shuttle has been shut down since 2011. But they had careful plans for disposal of the ET. For missions to the ISS, the tanks impacted in the Pacific Ocean. $\endgroup$
    – Organic Marble
    Commented May 15, 2020 at 21:23

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  1. Would this then be regarded as a single-stage-to-orbit, and a survivor of astronaut Don Petit's tyranny?

No, Long March 5B uses strap-on boosters. From a certain level of abstraction, there's little difference between a two stage rocket and a one-stage rocket with strap-on boosters. I believe the core stage engines are ignited at liftoff, but it's hard to be sure watching the video -- the kerosene/LOX plumes of the boosters are much brighter than the core stage exhaust would be.

  1. Are core stages going to start falling unpredictably from orbit† somewhat regularly now?

Yes, as upper stages have done for some time.

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    $\begingroup$ got it, thanks. I guess my concern is that first stages may have more and/or more massive potentially survivable chunks. Ever since my "Skylab is Falling" tee shirt days I worry about anything that can't be stopped by an otherwise-reliable layer of aluminum foil in my hat. $\endgroup$
    – uhoh
    Commented May 10, 2020 at 5:40
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    $\begingroup$ I happened across an article about a PAM-D stagefall while working on an answer to another question -- about the same size as the largest intact chunk of Skylab. $\endgroup$
    – Russell Borogove
    Commented May 10, 2020 at 14:16

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