As to why, probably because tellysinny sounds like one word, and cannot be mistaken for two or three discreet words. (unlike Tell a Sinner, or Telly Sign, or Tell a Sign or Tell a Sin)
Also:
a) It kinda rhymes (telly, sinny)
b) The abbreviation of television (when not TV) was already "telly" as in 'turn the telly on', no one says 'turn the tell-uh' on.
But tellasinna sounds like Tell a Sinner which is confusing and the uh sound on the end is ugly.
c) Tellysign sounds like a sign of some description to hang on the telly. Tellysign also follows no rules any way, not many people say sign-ema for cinema.
d) I think most English countries pronounce the first syllable of cinema as (roughly) Sin.