That's clever, but maybe those disks wouldn't work, same as the phasers didn't work. Also, could be that preparing certain kinds of tech wouldn't help either. For example, maybe the phasers would stop working as soon as they were prepared.
SPOCK: Sir, you are employing a double negative.
The phasers didn't work for Spock and McCoy, who had not been "prepared." Yet preparing anachronistic items will stop them from working? Huh?
I expressed exactly what I meant. I said, "Also, could be that preparing certain kinds of tech wouldn't help either
." There's no reason to conclude that the phasers must work, even if they were prepared.
That is to say, if someone wrote a sequel in which hand phasers didn't work even if they had been prepared, then that would be perfectly consistent and plausible based on everything we saw in the episode. No examples of them working after being prepared were shown in the episode, so it's wide open
for how a sequel handles the question.
There are any number of reasons that could be imagined to justify this behavior, if needed. Just to name two off the top of my head: maybe the act of preparing phasers shorts out some key component immediately; perhaps the Atavachron is based on certain theories of physics in which values assumed to be physical constants aren't really constant.
And, for the record, the constructions of mine that you highlighted are not