After posting, I remembered one important one, electrical resistance. That
might strongly reject austenitic stainless as a choice, if the antenna is
small or otherwise makes low resistance critical.

On the other hand its high strwength to weight ratio might be another strong
plus to add to any others, it can save nasty accidents with underestimating
wind loads, breaking strains and such when testing a new build. (For wires,
I'm less sure about towers, I haven't learned enough to make suggestions for
materials and structural forms and dimensions for those).