By far their most useful application is precision thermal control. Need that LED or laser to be within 0.05C to maintain its wavelength? Literally nothing else can do it.
Also camera sensors. AFAIK most (all?) high speed sensors are actively cooled with TEC. All high sensitivity cameras are, most telescopes and satellite cameras also i think
The highest sensitivity cameras tend to use cryocooling rather than TECS. But you're correct that a lot of mid to high end astro cameras are Peltier cooled, and many hobbyist imagers. Satellites are a mix, you have to get rid of the heat, so some missions also use cryocooling and are limited by the amount of cryogen on board. Some instruments also get away with passive cooling, if you can radiate it fast enough.
Yea, plenty of cameras need precise temperature control too. A laser or LED shifting spectra is just the easiest and most accessible example I could think of.
Highspeed needing it is a head scratcher though. Best I can come up with is the sensor needs relatively low temperatures, that or as the frame gets smaller on the sensor to up the framerate the power density goes nuts.
Also sensors with long exposure times, which are cooled to reduce the dark current. Amateur telescope camera chips are often actively cooled for long exposures.
interesting to know that there are actual critical applications for this technology though it does have limitations as I think the JWST is cooled with some sort of exotic compressor useing liquid helium, though perhaps a solid state device is part of the stack as they are after a very low, very stable temperature
The way these systems are controlled (in my terrestial experience) is to have the system be capable of cooling below the desired set point. Then you can PID the temperature using a heater or a thermal bridge/heat switch that will cause the system to warm up. It's complicated, and a lot of very interesting thermodynamics involved.
It also depends if you just need "as cold as possible" or if you need to know the temperature and can calibrate out fluctuation, or if you genuinely need stability.
