Usability testing with multiple devices in the same session with the same user?

We had a pilot test of usability testing. We only planned to do tests on desktop pc because that's what we think is the main device with the our user group.

After the pilot we had a feedback conversation with our teacher. One of the suggestions he made was that we should add some tasks that are done with the mobile device.

I disagreed immediately but couldn't come up with any good explanation why this is a bad thing. My opinion was not taken seriously because teacher is 'the pro'. Now I would like to know if this really is a standard testing method to have multiple devices in the same testing?

For me it slunds like finding issues here and there and not focusing anything. So you most likely find more issues but wouldn't it be more important to find the 'famous 80 % of the problems' with one device? In my opinion the experience with the first device affects to the use of second device because the system being tested is only a part of a website.

In our case we cannot have more participants.