Anything the NES graphical hardware displays is always broken down into four color 8x8 CHR tiles, there's not another option. Anything different than that is a creation of the programmer rather than a function of the hardware.
Programmers introduce the concept of 16x16 tiles to their engines because each 16x16 region of the "map" can only be one of the four 4 color palettes anyway. But to the hardware, those are separate concepts. There's not a limit on the unique 16x16 pixel regions that's like the 256 8x8 tiles in memory limit. The entire screen can be unique 16x16s (so long as they are still made of only 256 unique 8x8 tiles altogether) without any tricks or special cartridge hardware.
I don't know if most games do what Indivisible does, but I would assume so. I think the costs of not doing so are greater than the benefits. (Obviously or I'd not have done it! :lol: )
I wrote a 600 word essay in response, and now I'm like, "Is this actually gonna be helpful?" So... let's try shorter. Indivisible stores four bytes for each 16x16 "tile" it has. A byte for the number of the 8x8 tile for each corner. So if it has a solid color 16x16 "tile", it stores one solid color 8x8 tile in the CHR tileset, and then it stores the same byte four times to define the 16x16 "tile". (The byte is whatever the number for the solid color 8x8 tile is.)
There's a way to not store the four bytes, by arranging your tileset in a pattern. This method basically treats its 128x128 pixel tileset as 64 16x16 tiles rather than 256 8x8 tiles. If you want to do that same solid color 16x16 "tile" with this method, you use 3 more tiles in your set than the Indivisible method (you end up storing four identical 8x8 tiles in the CHR sheet), but you save the four bytes. Saving four bytes at the cost of three unique tiles is definitely not a fair trade, I think method 1 wins for free in the solid color tile test.
Now, most tiles won't be solid color. And method 2 wins when the 16x16 tile is fully unique. But, to me, in the cases where method 2 wins, it barely wins. And when method 1 wins, it soundly wins. Method 2 is a commitment to less graphical versatility to save space, but the space saved to me isn't even a lot. Definitely not enough to be worth giving up the versatility. There are other ways to save space that give up less. Just one person's opinion!
Closing note: There aren't really just two methods, you can mix and match the two described here or do whatever since only the 8x8 tiles are a hardware concept. The rest is software.