Wider aperture means bigger lens, especially zoom. This can be a negative for the non-professional who wants to minimize size/weight when travelling or just walking around town, especially if they already have a smaller, mirrorless body. Professionals, obviously, will use whatever size equipment they need to get the job done.

All the more reason to move to primes ;).

Seriously though, the comment about focusing on lenses instead of bodies is spot-on. Photography is the art of manipulating light, be that via off-camera flash, better lenses or picking the right time of day.

Getting a fancier camera body only lets you pick up the electrons that are already there, you'll see much larger improvements in your photo quality if you focus on the other things first.

In my experience, wider aperture often means slower focusing. The focus motor has to move a much larger piece of glass and focus with an even narrower depth of field.

That's usually the opposite case, wider apertures mean more light which gives the AF system more to work with. The AF speed of my 135L drops significantly if I put a 1.4x teleconverter on it despite needing to move the same amount of glass.

Most wide-aperture lenses have larger AF motors to compensate with the exception of a few unique lenses that use a gear instead of servo motor(USM in canon parlance).

That only works when you want subject separation though.