Many many reasons exist to buy lenses slower than f/2.8.

• Price
• Size
• Specialty lenses
• No need for a wide aperture
• Versatility
• Compromise over above factors

As you suggested not all types of photography require wide apertures. Landscape photographers oogle over the Canon TS-E 24mm f/3.5 L II Tilt-Shift Lens for example. It is f/3.5, costs around $2,000USD, and is of extremely excellent quality in all regards.

Another reason is simple "business sense". A pro doesn't buy f/2.8 just to buy it, they buy what they need to make images as their clients and work demands. You might be able to use a 70-200mm f/4 IS lens to get excellent images. Would spending $2,000 USD on a f/2.8 version of that lens produce more income for a professional? That is a question they would have to ask themselves before simply spending money for a heavier and bigger lens.

Versatility is a big one. Take for example the Canon EF 100-400mm f/4.5-5.6 L IS USM Lens. It is extremely versatile. Could you get the big 100-400mm in a f/2.8? Possibly, but I doubt it would ever be this size or image quality. The tradeoffs are worth it in this case to have such a focal length range. You aren't going to be shooting indoors with low light with this lens, but that isn't what it is for.

Regarding Your Edit

You can "get away" with slower lenses doing just about anything. You are just going to have to bump up the ISO, potentially use a tripod, flash unit, or multiple exposures to get a shot. Can you shoot sports indoors at f/5.6 without a flash and with a camera that is poor at high ISO performance? Probably not very well, but you can probably do it. But you probably can't shoot very great photos with a poor high ISO performer, no flash, and a lens that is only f/5.6. Take for example a current smartphone. Can they "get away" with capturing an image even in poor lighting and poor effective apertures, yes. But the results are poor.