10 bit is even better according to all these criteria AND it fits 0-1000 into one byte which meshes really well with metric system (0 to 1 km in meters, 0 to 1 liter in ml, etc.)

You could even do binary-encoded-metric-numbers that you can decode as needed one byte at a time - the first byte is tonnes, the second is kilograms, the third is grams, the 4th is milligrams, and you only lose 23 out of 1024 values at each level.

Same (but without loses) with data sizes. 1st bit is gigabytes, 2nd is megabytes, 3rd is kilobytes, 4th is bytes.

And of course at one point many computers used 40-bit floating point format which would fit nicely into our 4 bytes.

10-bit bytes would consist of two 5-bit nibbles, which you could use for two case-insensitive letters (for example Baudot Code was 5-bit). So you could still do hex-like 2-letter representation. Or you could send case-insensitive letters at 2 letters per byte.

40 bit could address 1 TB of memory (of 10-bit values - so much more than 1TB of 8-bit values). We could still be on 4-byte memory addressing to this day which would make all pointers 4-byte which would save us memory.

And so on.

But ultimately it always had to be power-of-two for cheaper hardware.