I can't cover all my uses in 10 lenses let alone just 3!
Given the chance to add 3 lenses to my current selection (without having to find the cash or track down a copy)
I might select:
the Canon MPE-65 or perhaps the Laowa 24mm/14 probe lens, (very different extreme macro options)
the Coastal optics 60mm f4 UV-VIS-IR APO macro (a UV lens with very little focus shift)
and round it off with a large format wide angle or (very different) a Sony FE 100-400mm F4.5-5.6 GM OSS
Even here adding specialist options to my existing hoard I've gone over the allowance of 3 lens roles!
I regularly shoot: IR, extreme telephoto, extremely low light, fisheye, macro... in addition to the typical roles a trinity might cover.
The IR shots might be OK with the trinity lenses but many top line modern lenses have hotspot issues, while cheaper or legacy lenses are generally usable.
Reflected UV is something I've tried but not yet got reasonable results with, it definitely needs a specialist lens.