On the web, we see a combination of multiple separate, independent systems, needed to produce meaningful artifacts for non-technical users. At the UI level, these are HTTP, HTML, CSS and JS. Three of these systems are stateless and each of the four is, in theory, independent of the others.
The combined artifact that these things work in concert to produce is often challenging to test. We already know that it's fruitful to test some of these systems apart from others. I posit that it's useful to break down some of that and test UI away from everything else and include design and QA in the conversation and methodology.
On the web, at the UI level, we have a combination of multiple because UI is a combination of multiple separate systems (HTML, CSS, JS). Each of those systems is testable by itself, but the combined artifact is often difficult or challenging to test.
For this reason, I suggest testing the UI alone.
If done well, your testing team can get confidence that they do not currently have, and the amount of time spent testing will decrease.
Of course, this means that you have to design and build a UI that can be tested alone.