I think the rotation (during the pedal stroke) happens with a lot pedals, but if it happens with essentially no friction at all (as is essentially the case with freshly lubricated SPDs) then it does feel a bit different. For 'something nasty' read 'something very slippy'. The rotation certainly does happen; if it cannot, my right knee hurts, (regardless of angle setting).
For at least the last thirty years I have had to file my right cleat slot into an hourglass shape, so that it will allow some twisting movement under load, yet won't flap around fore and aft, as it would do if the slot were simply cut wider.
When I ride with flat shoes, my right shoe exhibits marks that tell me that (unlike the left shoe/pedal) it isn't always presented to the pedal at the same angle under load.
When I ride with SPDs, even in town (where I am constantly unclipping with the left foot) the RH binding still wears faster than the left, because of the twisting in the right foot.
BTW there is meant to be some float with standard SPD cleats (SM-SH51) in standard SPD pedals. I use nearly all of it on the right foot. However, NB; pre-1997 SPD models have different jaws to later SPD models. There is less float with the standard (pre-1997) cleats and if you use old model SPDs with newer cleats, there is about zero float; the cleat is held almost completely rigid in the pedal.
[Confusingly the pre 1997 standard cleats were also marked SM-SH51, but if you have ever seen a pair side by side with current SM-SH51 you will see that the shape is different. Irritatingly even the current SM-SH51 cleats come in two versions; the difference lies in the placement of the teeth that grip the sole. Current cleats are slightly different to those that were made ~1997-2002, and when they are replaced, they don't sit in the teeth marks in the shoe sole perfectly.]
I have had the chance to observe many hundreds if not thousands of other cyclists pedalling at close quarters. I would say that the number that twist their foot in the downstroke (with one or both feet if they are allowed to move), greatly exceeds those that don't. If these people are forced to use floatless cleats in clipless pedals, moderate to severe knee pain is the inevitable outcome. Some folk get knee pain even if there is movement, but that movement requires a little too much force.
IIRC the LOOK system came with black (i.e. floatless) cleats only for the first few years and plenty of folk I knew tried and rejected the LOOK system because (regardless of cleat setting) it made their knees hurt. When red (floaty) cleats came out, most users quickly changed to those instead; for a while you could barely give black cleats away; happy days for those few that were content with them.
A side effect of having red cleats in the original LOOK pedals was that the length of time it took before the pedals started to squeak (uncontrollably) reduced considerably; the original pedals were not designed to have a moving cleat in them and once the metal claw parts lost their coating, a dry cleat would soon rub and squeak. Some users used a little spray lube on the cleats/pedal every ride but if it was wet it could be less than two hours before the squeaking would return. The same riders reported that if they used black cleats they would squeak too, suggesting that once the cleat/pedal was worn, there would be enough movement to allow squeaking even with 'floatless' cleats.
If you have a LOOK pedal with floatless cleats that squeaks, it may mean that there is vertical movement (which could be shoe sole wear not just cleat wear) and this is allowing enough movement for squeaking. However IME it is at least as likely that actually one foot (or both) wants to twist in the power stroke and that is why the thing is squeaking.
If you need about five degrees of float then there are lots of pedal systems that will accommodate you. If you need five degrees of near-frictionless float then there are fewer choices. If you need about ten degrees of frictionless float then the number of pedal systems that will accommodate you is very small indeed.
FWIW the speedplay pedal system has its adherents; lots of near-frictionless float, different length pedal spindles, and potential for camber adjustment between the shoe and cleat.
However if you want to be able to achieve these things on a budget, others (such as the SPD system) can also accommodate you, at significantly lower cost; pedals may be extended using pedal extenders, cleats can be modified easily to give more float and small camber adjustments can be made with insoles.
The SPD system (and one or two others) give near-frictionless float simply because the cleat is small; this only works perfectly if the cleat is properly positioned; wider pedal bodies allow an imperfect fit/cleat position to be tolerated but this usually comes at the expense of float friction.
BTW I think that the twisting of the foot can come from the knee and/or the ankle; e.g. in the latter case if the foot's arch deforms under load and in the former case if the axis of movement of the knee joint is not at exactly right angles to the centre plane of the bike/crank circle.
cheers