All these conversations are lacking a discussion about the atmosphere on Arrakis. We have only hints about the composition and density of the atmosphere. We can assume that the atmosphere isn't toxic and contains quantities of oxygen and carbon dioxide that make breathing both possible and comfortable. We can be sure it doesn't crush humans or explode their lungs.

We also don't know the gravity of the planet. It might be 1.2g or 0.85g.

So we don't know how much lift is generated per stroke, how much lift is required, or what the speed of sound actually is on the planet.

Ornithopters seem to be an Imperium-wide vehicle and not a Arrakis-only device which blunts the urgency of these questions and variances.

To be used on many different imperium planets seem to imply that it operates across an acceptable range of gravities and pressures, etc.

Ornithopter is a type of vehicle. It's unlikely any specific vehicle of the type would be generic enough to operate across the variety of planets that likely exist within the Imperium without modification to the design.

This particular branch of the discussion was focusing specifically on the feasibility of the 'dragonfly' ornithopters operating on Arrakis as represented in the new film.

The problem with the supersonic tips is identical for normal aircraft propellers.

For aircraft with fixed wings for generating lift, the propellers can be small, so supersonic speed is reached only at a higher rpm, but for a helicopter there is no difference from this point of view compared with an ornithopter.

The blades of a helicopter propeller must also be able to rotate along their longitudinal axis, like those of an ornithopter, but nonetheless they are more efficient than flapping wings, because there is no dead time and no energy lost for the reversing motions, and the fatigue resistance need not be as extreme as it would be required for flapping wings.

In the dune universe they have some kind of antigravity technology, so perhaps this is used to dampen the shockwave at the tips?

In our universe given enough power there is probably a way to generate an opposite wave to counter the shockwave.

But if you have antigravity, why do you need wings?

(Same also applies to having force fields, but the whole “slow blade” vs fast blade thing is enough to at least handwave that away)

Possibly cost. But also suspensors only seem to give lift, or very small amounts of lateral thrust. All the pure suspensor vehicles we see move extremely slowly. It's possible the 'thopters use suspensors for primary lift, maybe 80% of vehicle weight, and the wings are just for manoeuvring lift and thrust.

The aversion to using force fields is more about their interaction with laser guns, when shot by one they cause an explosion equivalent to a small nuclear weapon. Not ideal to have wrapping a vehicle you may be flying in formation on an attack run.