Yes plate capture, even large easy to read EU plates are a problem at night, in general i say you can do it, if the difference in speed between your camera and the target plate are slower than you can crawl on all four.
If you notice sales videos demoing night time footage, you will notice.
1: it is in a town with severe light pollution ( high levels of light at night )
2: the plates on the other cars you can actually read just fine, well that car are just very slowly passing buy in traffic, or the camera car are slowly passing it.
You Americans have additional challenges.
1: your plates and the lettering on them seem smaller than EU plates.
2: often all kinds of silly background graphics are allowed ( EU plates are reflective white with black letters, any graphics like your national identifier letters like DK in my case are off to the left side )
3: often cars have just 1 license plate, in the EU cars must have two
The reason you get blurred plates are motion blur due to the slow exposure timing ( 1/30 second ) the camera use in order to provide you with fairly bright footage.
In general photography it is said if you want to take a picture of something moving at speed, you need a exposure time of at least 1/500 second.
And your dashcam can do that just fine,,,,, in daylight, but at night using a exposure time that fast will just give you a black frame as thats far too fast for the sensor to catch any amount of light to work with.
Your camera is as good as it get with current technology im afraid, so a good habit at night is to see the plate yourself and call it out for the microphone to record.