As I often tell people; a LUT can only reduce the dynamic range of a display. For the most part that needn't matter, particularly if you have the whole of the DCI-P3 (or a decent chunk of Rec.2020) in your monitor. Applying a look-LUT to simulate a delivery style is one thing but increasingly people see LUTs as the first answer to monitor calibration rather than getting the display to as close-as-possible before profiling/creating a LUT. Hugh and I did a podcast on the subject.
A problem I've recently discovered with a monitor's internal Rec.709 LUT is that although the monitor has a huge gamut in it's native mode (which you can see from this recording of ChromaSurf's output) but the 709 presets have trouble.
Notice how it can reach a full green value of 0.1879, 0.7317 (Rec.2020 calls for 0.170,0.797); you'd think there would be absolutely no trouble getting Rec.709 right, and in fairness the primaries are fine. BUT, when I use both primary and secondary colour ramps;
I wind up with some distinctly funny looking banding in the secondary colours.
On this 'phone photo it is particularly noticeable in the yellows, but it's there in the cyan and magenta ramps as well. The fault isn't there when the monitor is in native mode (or indeed P3, NTSC or EBU), only Rec.709 (ironically the only colour space we really need for TV!).
So, I'll have to profile it in native mode and spin a 17-point 709 LUT as the one from the manufacturer is clearly got problems.
Another way of stress-testing a LUT is to use the TrueColor LUT stress test image.