Hands you hate to admit you played (LC)

[ALL1N]

This is not a "maths" situation. It is simply a matter of 3 things:
1. There are a lot of nice looking hands that like to fastplay the flop with you (such as pair+straight draw).
2. The board could deteriorate (4-straight), causing you to lose action from a lot of hands.
3. Your opponent will still feel the need to showdown if you fastplay, because you could easily be semibluffing a straight draw.

Fastplaying the flopped straight here is the best play here by no short measure, just as it nearly always is HU.