Most important antenna design and analyze tool for the real antenna, not the simulated one, is for me a VNA.
As I mainly design multiband handheld embedded antennas is AnTune my most important software during development phase.
In most cases have I to accept existing very limited antenna space, a too small ground-plane and dead-line is passed from beginning.
No time for simulation then and as PIFA is a good enough alternative in 90 % of these applications is quickest solution to start working directly with hardware.
During development phase do I need a software that takes care of antenna documentation so I easy can compare minor hardware variations.
Small embedded antenna development must focus on best possible bandwidth and efficiency, whatever impedance it result in, so an impedance correcting network is a must. For that do I need a software that can tell me continuously during development-phase if a such network is possible within a simple PI or T network, without costing me any time.
Designing a wide-band antenna, and afterward try to implement a matching network for compensating poor VSWR at band-edges, without affecting mid-band too much, result in that neither antenna or network is fully used for highest efficiency and best VSWR. Do maybe work for a tri-band antennas in conventional phones, but in a modern smart cellphone is space less and requirement for bandwidth much higher so eventual improvements from a impedance network must be be better used then just to do minor adjustment of band-edges.
Nothing wrong with to do deep pre-analyzes/design but should these be anything worth for me must I simulate a complex hardware including different types of body-loading effects. It is an exception if I even know what dielectric constant the plastic that covers antenna have, so in daily production must I, just by looking at hardware for a few minutes, be able to get an idea how an antenna with best possible efficiency can be shaped.
So that is probably the most important tool, the analyzer I have in my head. After a day or two do I usually find that it was a less good judgement I did from start, but a simulation tool had not done a better job either, as it neither delivers better result then what the user is able to provide.