Yes and no, your display 'sees' linear gamma but, it's using an SDR gamma container because it's completely predictable and we know that almost all displays can replicate it properly and you can generally trust its somewhat right, but every displays eotf rendition is totally unpredictable, the DTM processor has absolutely no idea what it would look like on your display, so the only solution is to map it to a linear gamma, but as said it's not linear reqlly., Your display this is it's linear, but the processed image is not and it does not suffer from any of the issues you mention.This I disagree. Isn't tonemapped "SDR container" signal linear though? I mean you are or should be using a straight gamma in projector so it has to be linear..
There is still a curve internally done by the tone mapper, it's an s curve. This means the highlights are suitably compressed and the low range expanded as expected, a good tone mapper will still have the correct bt2390 rolloff etc.
First thing we did with madvr was to get it to look absolutely identical to the Arve curves, so much so we actually fed madvr the Arve curve itself and it output that in SDR. It was completely identical to the pq Arve curves on my JVC. Once we did that we had a good foundation to work from and could finally ditch the HDR mode on the projector and start working on making it dynamic.
Like was said before, you REALLY need to stop thinking about it as SDR.