It is true that in more modern computer architectures, 8 bits is roughly synonymous with a single byte. However that doesn't always mean that we count things in bytes.
Think about a soft drink, maybe a Coca-Cola or something. What are some typical sizes it might be sold in? I will use my memory of Japan and the US as examples:
375 mL ~ 12 fl oz
500 mL ~ 16.9 fl oz
20 fl oz
1 L = 1 L
2 L = 2 L
Notice that, even on Japan's side of the chart, we're switching between units: milliliters and liters. ...Could we just as easily say things like "1000 mL" and "2000 mL", or either ".375 L" and ".5 L"? Yes, absolutely!
Then why don't we? Because as the general size of the drink container is scaled, the units that we find most useful scale with it.
So think of the NES, which was an 8-bit system. Later you had the Sega Genesis and SNES, which were both 16-bit. The original PlayStation was 32-bit, the N64 (Nintendo likes abbreviations, don't they?) was 64-bit, the Sega Dreamcast was 128-bit, and so on.
Have you ever heard of a normal 64-byte or 128-byte computer architecture? No, of course not. Even the Sega Dreamcast and similar systems had merely "8-byte" architectures. And as other answers have stated, 8 bits hasn't always been completely synonymous with a single byte.
(And to be completely pedantic, 8 bits aren't exactly the same thing as a byte on anything, since they could each belong to different bytes, if you just pick them out randomly. A byte is technically an ordered collection of bits.)
Think about how tiny a single computer instruction is. It is small compared to a lot of what we would normally count in bytes. In fact, when you're dealing with Assembly, you're dealing with quite a lot of detail, including individual bits.
So in the same way that we go from measuring soft drink sizes in liters to milliliters, just because of the scale being different, we go from measuring things in bytes and gigabytes to individual bits, just because of the scale.