Depends entirely on the TV. There's nothing Sony can do here.
Before I bought mine, I was in the middle of doing some research, and a website called
Rtings.com alerted me to the fact that TVs have different response times dependent on the mode - whether that's 4:4:4 chroma, HDR, 50hz, 60hz or whatever.
So when you see a review of a TV and it states the response time, that's just
one response time for
one resolution, refresh rate, chroma, etc. etc. etc.
Here's an example of their input lag measurement for a Samsung KS8500:
(The only important figures here are all the 4K ones, because the PS4 Pro upscales and outputs everything in 4K.)
So even with "game mode" enabled, there is a significant difference in response time depending on the input...
With this TV, HDR doesn't increase input lag, BUT... 4:4:4 chroma does. So if you want to lower response time with that TV, you're better off setting the PS4 Pro to be in 2180p YUV mode - you'll miss out on 4:4:4 chroma, but you'll get a lightning response time.
If you find 30ms+ is too laggy for you.
This is one example, out of hundreds of 4K TVs...
If you haven't bought a TV yet, but you've got one in mind, try and find all of these figures for all of the modes first.
Either way, Sony can't magically make this TV have faster response rates, and the same applies for those TVs where enabling HDR totally screws the response times.