Actually, for most of its existence, Cyrillic has had a θ (theta) like in Greek, used only in loanwords and pronounced either as ф (f) or т (t) because the th sound is not part of Slavic phonetics. θ was dropped fairly recently - in the 20th century.

It absolutely doesn't as pronounced now, yet Thomas is Фома, Theodor is Феодор, etc. Just like Hertz is Герц, even through Г and H are as far from each other as one can get.

Yeah, it is just фe most aesфetically pleasing letter for фis case.