Isn't as simple as that really, and what you've said isn't really how the commercial world works in reality tbh.
in a very basic sense, for long term viability it's certainly better to go with an established brand offering less money than an obscure brand offer much more. Obviously there are lots of variables to consider but for a club like Arsenal it's smart to go with established brands even if it mean less money.
Smaller clubs take who offers the most cash hence why you see JD, Sandico, Carbrini and dryworld at the bottom end of the league and championship. Nike and addidas usually go for lower league clubs with a strong brand
You'd be surprised how deep the brand stuff goes. I used to work at Sportsdirect and people constantly asked where they could find the Nike huarache in store, I told them you have to go to JD for them. Nike wouldn't stock SportsDirect with huarache trainers even though a huge demand was clearly there.
Nike didn't want their top fashion shoes associated with sports equipment and sportsdirect other homegrown crap. JD stores was an established and dedicated fashion store with a strong urban brand and young customer base that stocked the best of other manufactures fashion shoes. Who know how much sales nike lost through customers taking other manufacturers shoes in JD but to Nike it's worth it in order to maintain a particular brand.
I'm just trying to highlight the molecular scale of how fashion manufactures operate in order to maintain a particular brand on certain products