I wonder if ballasts that say they require circuit interrupting lampholders operate lamps properly WITHOUT circuit interrupting lampholders?

They do, I think the only reason for the circuit interrupting lamp holders is so the ballast gets disconnected from mains when the lamp is missing. Some ballasts (like slimline ballasts) can suffer damaged if they're connected to mains with no/non-working lamps. NPF single lamp rapid start ballasts also use circuit interrupting lamp holders, but i'm not exactly sure why they do.

It is not that much about damaging the ballast, but to prevent lethal shock during handling the lamp with the fixture powered.
These ballasts have rather high OCV, with capability to deliver 100's mA, co pretty lethal combination.
The idea assumes, the sockets are made so you can not touch anything live on the sockets, nor anything live on the lamp if it is in the socket so it makes contacts.
The problem is, when the lamp is inserted only by one of its ends, so the pins of the other one are exposed to you to touch it.
If the inserted end is on the "cold" side (so with no more than 120V vs ground), the lamp wont conduct any electricity, so even when touching the exposed pins on the other end, nothing happens.
But when you insert the hot end and touch the other lamp contact ends, the high voltage ignites the lamp and makes it conductive, sending the dangerous voltage to your body.
Now when the cold end socket disconnects the feed when the lamp is not inserted there, the situation when only the hot end is connected to the becomes not dangerous, because there is only the mains voltage at that hot end and that is not enough to ignite the lamp, so the lamp remains nonconductive, so its cold end pins remain rather safe.

Classical preheat ballast needs the starter circuit to complete first, so without connection on both ends it wont preheat and ignite, so it is safe.
Lead style RS ballast make the lamp conductive only in one direction (when the inserted electrode is a cathode) and hence it uses the series capacitor, it is enough to not allow any current to flow.
Residential ballasts are more problematic - because they are DC conductive, so happily shock you with the one half wave. But still we are talking about rather limited voltage (compare to the cold starting slimlines).

Electronic ballasts in most of the civilized world (looks like except US) require the ballast to not operate when only the hot lamp end is inserted. Apparently the US code is satisfied with the HF not being that dangerous as the low frequency is, so all the IS ballasts with just one lead per lamp end (so in no way able to distinguish correct lamp connection) are legal...