Yes but then you want to see if the CPU mater in a representative case. I mean do you go and buy a car based on a dyno run test which while give lots of information it is in no way representative of real world performance?
Rule number one: car analogies always fail; in this case, because you're not testing the car, but you are testing the ENGINE of the car. If you test higher resolutions, to keep with your car analogy, the other components of the car come into play, that determine if the car won't fall apart at the top speed the engine can achieve. In the latter case, you move the testing towards the components surrounding the engine as they will always be the limiting factor in one way or another.
You want to see the limitations of the CPU, and the maximum performance you can extract from it. Because that is what a CPU test is about. Alongside that, one higher resolution is sufficient, and in that case I would still vote for 720p + 1080p. Perhaps 720p versus 1440p would do fine too.
Once you crank up the resolution, you move the bottleneck towards the GPU (even at 1080p on a GTX 1080, this can happen, will happen frequently) and at that point you are no longer 'testing' the CPU performance, but the GPU performance on that specific CPU.
'Representative' is irrelevant in this case because it simply does not exist. The only representative test is testing your own content on your own setup. Performance testing is never and should never be about 'representative' because everyone has a different setup. You can never tick all the boxes. RAM at a different speed? Different outcome. Higher GPU OC? Different outcome. GPU on water? Different outcome...
Testing at 1080p/1440p/4K makes 2/3rds of all benches you run effectively useless, as in, they provide no meaningful information compared to the test @ the lowest res of the three. The CPU will do the same work on all three resolutions. And even on the lowest res you can't get a view of that maximum FPS a CPU can push out.