The very short cotton socks which one wears with trainers are to make it more comfortable, so not putting your 'sweaty' foot next to a synthetic insole. They are not meant to be seen, hence the shortness.
But I agree, socks with sandals, flip-flops, long or short, are a no-no.
The second photo with the red/green/black jobbies are OK. A fashion statement, or a Christmas/birthday present from a wife or GF.