Only if you refuse to accept the salient facts / truth of the matter
As I have already explained, if you have two display devices that are matched and set up and calibrated the same then yes the two images will indeed look identical
However, it is important to note what I have said regarding the devices being MATCHED
. This means that the technical performance capabilities need to be the same. You can't calibrate an IPS Panel LCD TV and make it look the same as an OLED TV, because it does not have the same technical performance capabilites. Similarly, you can't calibrate a SONY 5000ES and make it look the same as an OLED TV either; wherein for example the peak contrast ratios, the color gamut coverage, and the peak luminance are completely different. However, there does in fact currently exist one projector which has essentially the same technical performance capabilties as an OLED TV, and guess what? When set up and calibrated properly it looks EXACTLY
like an OLED TV!
In short, if both devices have the same technical performance capabilities this would enable you to set up and calibrate both display devices such that they look the same.
And here's the key point you are missing, whether the devices are emissive or reflective IS IRRELEVANT
When you are comparing your projector versus your TV you are comparing two devices with completely different technical performance capabilities, which are probably not calibrated either, and with different settings. This is about as much of an Apples vs Oranges comparison as you can get. Consequently, the difference that you are seeing, which is the root cause of your personal preference, is due to a combination of the different technical performance capabilties plus different calibration and settings. It has NOTHING to do with the fact one is an emissive video display and the other is not.
Furthermore, regarding TVs in their own right, as I have already said, if you are finding a TV to be eye fatiguing in any regard whatsoever then this has absolutely NOTHING to do with the fact it is an emissive display, but because the TV is not setup and calibrated properly, including with respect to your particular environment. Seriously, attend an Imaging Science Foundation (ISF) or Professional Video Alliance professional video calibrating training course and you will be told this on DAY ONE.
You are just plain wrong about this, sorry! In short, the science does not agree with you!
But if you want to (incorrectly) believe that all emissive displays cause eye fatigue due to being emissive, then please by all means go right ahead