Why do dental drills need such high rpm?

I got this answer from a friend who is an orthodontic surgeon.

Without consulting Wiki (incomplete article) - I can say this off the top of my head - The rpm is closer to 400 K.

The speed is needed to give the bit/burr some rotational momentum to provide torque. There is no direct connection between the source of the energy- compressed air - and the burr. The compressed air is only at about 2.7 bar and spins a turbine in the head of the drill, which the burr is attached to. You can hold the burr with your fingers stationary from start-up - no torque like a concrete bit. Another mistake in the question is that unlike a concrete drill - most of the cutting takes place on the side of the burr from a sweeping motion, not at the tip pushing down on the rotational axis.

What I described here is the high-speed air rotor. The one that makes the high pitched whine. It has water cooling and lighting (optic fibers or piezoelectric) built into the head. It is used mostly to remove enamel with minimum discomfort. The "slow" handpiece - up to 200 K rpm has a motor with direct drive through gears to the burr. Can also have water and fiber optics. Much more torque and vibration. Does not cut enamel efficiently. The motor can be driven by compressed air or electric- more control and torque- more expensive. The handpiece can be "regular " to remove caries mostly. This is known as a Contra angle handpiece. More sophisticated ones are required to place implants and do endo/root canal treatment. On the same drive system you also fit a straight handpiece used to cut bone in surgery. Then you can also cut bone with a piezoelectric handpiece or a laser.

The one type (air rotor) that I assume the question was about - is described as an "abrasive device" - not a "drill" as I pointed out. They also come in the regular head (more torque) and small to reach inaccessible areas (less torque).

Air Turbine Handpiece

An air turbine handpiece is highly valued as a dental abrasive device that rotates at a high speed, and it is an essential device for dental treatment. Since its development, many studies have been conducted to measure and evaluate rotation performance and measure and evaluate noise. An air turbine handpiece uses compressed air as the driving force and is characterized by its small size, lightweight, and painless abrading at a high rotation speed. However, compared to an electric handpiece that uses a motor as the driving force, its torque is small and the noise level is high.

As such, improved performance and reduced noise for an air turbine, handpiece are desired. Considering that an air turbine handpiece has the equivalent rotation performance as turbine performance, it can be considered as a type of turbomachinery, and the fluid mechanics approach would be effective. In other words, it would be effective to first elucidate the internal flow of an air turbine handpiece and the relation between the performance and the noise characteristics and then control the flow. However, the main component of an air turbine handpiece, the rotor, is small and rotates at high speeds (250,000–400,000 min−1); thus, measuring the flow is not easy.

The whole subject is obviously a lot more complicated than the question posed by the OP. I think my off-the-cuff answer is adequate without going into too much technical detail.

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