Telegrams have a quaint connotation these days I suppose.

In old Indian movies, a Telegram would only arrive to signify really bad news - someone died, or something like that. Why else would you pay for that expense? Well, it could also be a job interview or posting. So the connotation there, in that time, was probably not so good.

In old Indian movies...

Old movies in general, Indian or Hollywood. For pretty much the reasons you list.