This makes sense to me and I think explains everything nicely.
I am not suggesting that Celestia has a deep and personal love for each and every one of her subjects individually. I am suggesting that she has a deep and profound love for all of her subjects as one. She may love a few specific ponies too, like Luna and Twilight, but that's besides the point and not what I'm thinking of here. Though no doubt her love for those two would also be strong and possibly something she could tap into if ever they were seriously threatened (with actual harm or something).
I'm willing to concede that she may need the Elements to harness the full potential of her Love (my head canon puts Love as a kind of Friendship and thus within the domain of the Elements), but we have seen for example in Twilights's cutie mark story that the magic of friendship can be used without the Elements present and even with all its wearers unaware of each other. Sure Twilight didn't have any control over it, but it's possible that this was simply a result of circumstances or Twilight being so young.
As I see it, the magic of friendship and love has a sort of life of its own and is likely to take over or surge in certain situations, probably dramatic situations in particular, but it can be intentionally focused to a degree but only to its full extent with the help of the Elements.