Well, there are some contexts where it is appropriate to translate to call as telefonál. For example: "Peti called; he can't come with us tonight." = "Peti telefonált (or hívott), nem tud eljönni velünk ma este."
But if you call somebody, "telefonál" doesn't work. "I'll call you tomorrow." = "Holnap felhívlak."
And you can't use hív when you want to express that the subject is talking on the phone. In a sentence like the one above, telefonál will be understood as "talking on the phone", while hív will mean "being in the process of calling someone".
I believe the automatic conjugation is only present for a handful of courses (German, French, Spanish, Italian, Portuguese or so) that were developed first -- all the dozens of languages that came later use a different technological basis and are missing some things that this first group has.
Actually, here in the U.S., you are right, we do mostly say "phoning" as a verb. But we also use "telephoning" and--you are right about this too--even "phonecalling." I hear all three, though mostly the first. I find Duolingo teaches not only the language I am learning but also the English I already know, especially through these nice comment conversations. You're very welcome!