A cheap diesel/gasoline generator might do like 5kW, which is enough for overnight charging but not for range extension or powering the wheels. There were several pretty good range extended EVs (plugin hybrid with larger battery and smaller engine), like the Volt and BMW i3, those had small engines that mainly acted as generators for the battery, but with enough horsepower to at least keep you rolling on the highway. A $300 modular generator ain't quite gonna cut it.
I believe there's also a bunch of Chinese vehicles with similar design, entirely electric drivetrain with gas generators for range extension. Most of these will need to kick in before the battery is empty so that there's some stored energy buffer available for acceleration.
To put it in perspective why a 5kWh generator isn't a range extender: my lightening has a range of 331 miles and 135kWh battery. If we assume a spherical cow (60mph, and I get every single one of those 331 miles), the truck buns through the battery in 5.5 hours, which equates to 24.5kWh to keep up.
In actuality, at highway speeds I'll burn through 80% of the battery in 3 hours which equals a run rate of 36kWh. If we ran a 5kWh generator the whole time and assume perfect charging efficiency, it'd extend the time to charge by 28 minutes.