They actually DO make "1ms" 1080p @ 60hz monitors. Well, they DID, at least. And even then, mostly it was via the use of marketing terminology around an anti-flicker or clicker-free type mechanism that only emulated such things (not referring to LightBoost, however).
I would say a better question would be....WHY?
If the standard response times that typical 1080p @ 60hz run at is that big of a concern (and I believe the best one would find in that arena would be 5ms with both IPS and TN panels) why wouldn't the preference be to evaluate the next step up with 1440p (2K) models with refresh rates that range between 60hz - 144hz (and even now with Asus having launched two, new 1080p displays that use both 180hz and one as high as 240hz). Even then, the best you would see with a low, native response time would be 4ms IPS panels on higher-end brands and 2ms TN panels on everything else.
I think response time is one of those factors that people look at, just like refresh rate. Some really can see the difference between 1ms and 2ms, but perhaps can't between 60hz and 120hz, and likewise, perhaps someone that may be more focused on the gains of a higher refresh rate (like myself - and this is the honest truth - I can even tell the different between my two 1440p displays with one at 144hz and the other at 165hz).
The only reason I could think that there would be a specific need to stay on the low-end of 1080p @ 60hz (and then try to find the best there is with the technology) would be to accommodate a lower-end GPU or perhaps some other, very specific function that absolutely requires the use of 1ms response time in a display?
Facebook
Twitter
Instagram