Conical benefits include; ease of closed transfers, hydrometer readings and trub removal without exposure to O2 (gravity vs siphon, etc). Also safer and easier to handle and clean, no exposure to light, ease of use tri clamp sealed fittings, could probably think of more.
Let's compare a "conical" fermenter to a basic plastic brew bucket with a lid that actually seals and spigot. I wouldn't use glass.
Closed transfers: CO2 in the top, drain out the bottom. Conical shape doesn't provide any benefit to this workflow. Some vessels like kegs or Fermonsters are certainly capable of pressurized transfers (with a little DIY on the lid).
Hydrometer readings: Easy -- drain sample from the spigot. Advantage bucket since trub/yeast might get in the way of the bottom drain on a conical.
Trub removal: I already covered this. Leave trub in the kettle and leave the yeast in the fermenter. Our yeast don't suffer from the same hydrostatic forces that affect commercial production.
Handling: Advantage bucket.
Cleaning: Ease of cleaning is difficult to quantify. Fermenters with more pieces are arguably more difficult to clean. I can rinse out my [extremely lightweight] Fermonsters by holding them upsidedown with one hand and spraying the inside with a hose. Overnight soak, no scrubbing, easy peasy. Spigot and lid disassembled and soaked separately.
Light exposure: Conical shape provides no advantage. One could make an argument either way whether an opaque or clear fermenter is better. It's basically going to be in the dark anyway since it's going to be in some kind of fermentation chamber and not out on the patio.
Fittings: I agree TC fittings are ideal for cold side fittings because of their sanitary nature, as long as you have no threads in the entire fitting. Still, a plastic spigot is also pretty easy to assemble and disassemble as well as install and uninstall.
Since yeast cake in properly managed conical is never exposed to O2, even after racking, it is also possible to put new wort in fermentor on a nice dose of yeast without even re sanitizing the primary vessel. So far I've as many as 3 back to back fermentations this way with good results. Not sure I would venture more between full sanitizations, (we will see how daring I become).
Oxygen exposure and intracellular CO2 removal is very beneficial to yeast before pitching. The intracellular CO2 removal takes time, a matter of hours.
Yeast are ideally pitched at high kräusen.
This brings up another possible benefit I'm not currently set up to exploit, which is true clean in place capability. Something I intend to set up for sure.
I'm actually not trying to be snarky by asking this, but why would be bother with CIP if it's so easy to clean already?
It's good you like your fermenter, and I'm sure it's quality, but saying it's the pinnacle of homebrew fermentation vessels just isn't true. Everything has advantages and disadvantages. I'm pretty sure a conical would be too bulky to fit into my fermentation fridge for example.