First, the Flat profile is indeed a log profile, and the gamma can be adjusted in the camera. And 10bit colors was available at the start even in 5.3K 60p. In Linear mode, there is hardly any fisheye, and at 5.3K resolution there is plenty of detail for 4K despite the crop.
But now with GoPro Labs firmware:
1. You can up the bitrate to 200 Mbps (HEVC, 10bit).
2. You can now shoot 4K 120p in 10bit (newest firmware).
3. You can turn off noise reduction - and you get visibly more detail, and any noise is actually very fine.
5.3K using 2.35:1 crop (10bit, Flat, Linear, extended color gamut (Native), 180 Mbps HEVC):
4K 120P 10bit, Flat, 180Mbps: