Not really. It depends on the ASIO driver in question. Many (most?) ASIO drivers are multi-client, meaning they can accommodate multiple audio generating applications at the same time including Windows system audio.
Here is a Steinberg announcement from 2012(!) confirming:
These examples are obviously out of date, but it proves that it is quite possible. I’m not sure why the UR44, in this day and age, has such a limitation and it surprises me.
I use RME interfaces and have been for the past couple of decades. Their ASIO drivers are top notch and have been supporting multi-client use for as long as I can remember. I can happily assign dedicated outputs in several applications and use them all at the same time.