If frienship = magic, then converse must be true

I just wanted to post a thought.
A lot of people in fiction equate being alicorn with power. Either being powerful (in terms of extraordinary talent or magical energy or whatever) causes pony to turn into alicorn or fact of being an alicorn gives pony extra powers, not meaning all types of magic, but sheer volume of power other ponies could not access.

And the supporting point would be Celestia, who is ostensibly a Goddess of nigh-insurmountable might, comparable to, if below the level of Discord and such.
Now it can be argued one way or the other, but I just wanted to say that perhaps Celestia is so mighty not because she is an alicorn, nor because she lived for thousands of year and would have been an extraordinary unicorn even before that, and not even because she is/was the wielder of all the Elements of Harmony.

Celestia is so powerful because she is Celestia. She is motherly, kind, knows everything about every pony in the kingdom (in a non-creepy way) and cares about all of them, and beyond all she is truly, almost without exception beloved by her subjects.
If Friendship is magic, nopony could be more magical than her, because she wields the friendship and love potential of entire Equestria.