That would be desirable but it does not happen in practice.
All the USB network devices that I have ever used required specific drivers. Sometimes the drivers happened to be already bundled with the Linux kernel or with Windows, but frequently they were not.
If you start the configuration of the Linux kernel and you go to "Device Drivers", then to "USB Network Adapters", you will notice that there are close to 50 such device drivers.
That should tell you that there are plenty of different USB Ethernet Adapters that you can find when buying one.
Among those that I have encountered more frequently have been several kinds of Realtek, and of ASIX, and of Aquantia.
Especially among the faster USB Ethernet adapters I doubt that there are many without custom drivers.
Some people may not notice this, if they are using only fat Linux kernels, with all the possible device drivers being enabled and compiled, but if you use a streamlined kernel, e.g. for instant booting, you may need to add a device driver whenever you buy such an Ethernet adapter.
Where do you buy such things? Every USB Ethernet card I've used in the last 10 years was either RNDIS or some version of USB-CDC. They've worked out of the box on both Linux, Windows and some even Android.