Well yeah, in this particular instance they do. That doesn't mean they always do. For example, with the commonly-used Tennessee capital election scenario (https://en.wikipedia.org/wiki/Instant-runoff_voting#Tennesse...), IRV would select Knoxville while FPTP would select Memphis - still not quite optimal for everyone (Nashville would probably be the ideal winner in a "perfect" electoral system), but good enough for the majority and a strict improvement over FPTP.
Contrived scenario for FPTP picking the Condorcet winner while IRV fails to:
Back to the "which theocracy, or do we just tolerance?" question, but now each religion has at least two candidates and secular tolerance has a bigger constituency.
19% S, ...
16% A1, A2, S, ...
15% A2, A1, S, ...
14% B1, B2, S, ...
13% B2, B1, S, ...
12% C1, C2, S, ...
11% C2, C1, S, ...
FPTP picks S, sort of by chance, which is also the Condorcet winner. IRV consolidates the C votes behind C1, then the B votes behind B1, then the A votes behind A1, then discards S.I think that works out, FPTP makes the right choice for sort of the wrong reason while IRV makes the wrong choice. But I do think the much bigger concern is FPTP-with-strategic-voting behaving better (or at least no worse) than IRV-with-whatever-happens-in-practice.
I'm failing to see how that's worse than FPTP, which in practice would also result in picking Theocracy A (because the 5% representing the Secular Tolerance Party would be one of those "third parties" which get blamed for spoilers under FPTP).