I apologize for the delay in answering (I have been engaged in surfing “Flood-waves” in this other thread).
The main objection in these “responses” you refer to against the discreteness or granularity of space-time (i.e.: the claim that “the universe actually has minimum size for space and time intervals” or “space-time is pixelated”) is the following:
“However, the issue here is not the existence of smaller time and length scales, but the observability of them. Given current technology and knowledge, we have no way to actually probe that scale at all.
It should be very clear that the inability to probe a certain scale does not imply the non-existence of lower level structure. If that were the case then we would have concluded that atoms do not exist just over a century ago, contrary to what we know today.
The strongest conclusion that might be drawn is that space and time have a minimal observable resolution. The issue of whether time and space are actually discrete as suggested here, is by no means settled.”
The fallacy behind this argument consists in assuming that space-time can be actually continuum while observably discrete because of a “minimal observable resolution”.
Space-time is the realm of all what is observable. If something is not observable in principle, it does NOT exist in space-time at all. Accordingly, assuming that there is a “minimal observable resolution” is exactly the same as assuming that “space-time is actually discrete”.
Recently I have posted this video:
I am interested in your opinion, if you find time to watch it.