Gainmaps only take a lot of space if implemented poorly in the software creating the gainmap. On Pixel phones they take up 2% of the image size, by being stored in quarter resolution and scaling back up during decoding, which works fine on all gainmap-supported devices.
They're more prone to banding, but it's definitely not a problem with all images.
I guess I should say, take up lots of space unless you're OK with lower quality. In any case, gainmaps are entirely unrelated to the 8 bit vs 10 bit question. The more range you have (gamut or brightness) the worse 8 bit is, regardless of whether you're using a gainmap or not. And you can use gainmaps with 10 bit images.
