Polycarbonate thermal expansion coefficient - 65 * 10^-6 per degree C (source)
Glass thermal expansion coefficient - 9 * 10^-6 per degree C (source)
Most amateur telescopes are used shortly after dusk when the temperature is changing more rapidly than deep in the night when the temperature might be more stable. Also, the coatings are not as resistant to more dramatic expansion cycles (remember that you need those mirrors to stay very smooth). Given the high price and low volume of the goods, it doesn't make sense to cheap out on a critical component like this and give yourself a bad reputation among a very small but dedicated community.
Low thermal expansion glasses/ceramics can have coefficients of thermal expansion of 0 (+/- tolerance). For example, SCHOTT ZERODUR can be 0 +/- 0.02 * 10^-6 per degree C.
Also, I can make thermals irrelevant easily with a small heating element and PID loop running on a $0.50 microcontroller. Many people run such elements already to avoid issues with moisture.
The OP said cost. A 16" glass mirror is $1400. Adding $20 of microcontrollers, heaters and sensors to a $100 plastic mirror could be extremely interesting.
There is also a weight savings which makes the rest of the design easier.
That PID heating setup would draw significant power over an observing session - you'd need a decent power station for field use (check gearscouts.com for options with good $/Wh on LFP batteries that wont die after a year).