I imagine it's a similar sort of thing to what happens in Formula 1 where different teams pick engine suppliers. Perhaps it was a thing at the start of FX350 to avoid a RIDS issue that the five 'established' teams made a generic use weapons system and were able to distribute it to other teams. AG-S had to supply Triakis (perhaps for no cost, since I like to think that while Triakis don't like AG-Systems, the Japanese have no ill will and feel pretty ashamed over the whole 'being gifted a world championship' thing), and Mirage bought a contract.

EG-X could still be experimenting with its' own things, the neural interface flying as seen as far back by eG.r in Fusion, so they'd want to keep it under wraps. Even if Qirex is under new management, perhaps enough money could convince them to look the other way at some of the less ethical parts of their allies' use of equipment.

Harimau most likely bought a contract with Auricom, no real strings attached. Possibly since they arrive late to the season (same as Auricom) it's a teething issue for both teams. If we're still doing role-play with FX350 ships, could easily say there's something wrong with Auricom's AI.

Piranha wasn't a particularly good performer in Pure as far as I remember, so very possibly their weapon system is the cheapest - and that's why Goteki 45 have gone for it, being back markers as well.

I think the FEISAR/Assegai tie up is just mutual understanding between the teams, I imagine they get on quite well. Both are managed by big international organisations rather than having one solid base, so having a system that's instantly understandable to lots of people regardless of language or traditions could probably make a lot of sense. Icaras is a different basket though, since I always assumed the history (I'll have to watch Hellfire's video again) was that Icaras did a takeover of one of FEISAR's plants so that's the one I have trouble making reasons why they'd be so willing to use it. If they were, I bet FEISAR is milking every last drop of cash for the contract, and maybe even trying to sabotage their Euro rivals so they can be brought back into the fold.