2ms is nothing. You wouldn't even notice 20ms lag, unless you are 15 years old
Sophia Rev.C itself does not introduce any extra processing delay.
When you use it with a PC Monitor, you will have very little lag (for example 5ms with Acer S200HLBbd, which is neglectable).
The most of TVs have a lag in a range of 100ms - 200ms in a normal mode, so you really have to remember to switch a TV to the game mode (to disable DSP processing) and you will end up with ~20ms lag.
Here is an overview showing example TVs lags:
Anyway, your ATARI with SOPHIA Rev.C can still be connected to a CRT (over Composite Video), so you don't miss anything.
In my opinion Sophia is the most efficient way to enjoy your Atari in a living room
I agree that the Sophia is a nice option to have moving forward as CRT's are becoming harder to find and more expensive.
And I also agree 2ms is not a huge lag time. I was sort of mixing two thoughts together above and I mistakenly said refresh rate when I meant response time(the rate at which a pixel can change color).
A 2ms response time however is very slow. The response time of a CRT's pixels is over 1000 times faster than an LCD. The only thing that comes close to a CRT's response time is an OLED/QLED at 10us, and right now those are quite expensive and that's still over ten times slower. And funnily enough they get screen burn in just like a CRT.
But anyways, I'm just saying when combing lag time with response response time, I get why people like to hold on to CRT's.