I'm not sure of this: I'd very much prefer a world where 0.01% of guilty people and 0.0001 of innocent people are convicted to one where 60.01% and 60.001% are.

So do I. This answers the question "do I consider false convictions worse than guilty parties who are not punished" but does not tell us much about the original question. The point of the original question was not "with trivial consideration of how much the conviction process is different to chance how high is the base rate of convictions for this crime?"

Huh? How else could the original question be interpreted?

That is a reasonable interpretation - the point is that we must also interpret 'significance' in light of the original meaning. That original meaning does not contain an overwhelming emphasis on the base rate of convictions!