Just want to respond to a few points here - I'm not saying your experiences are "wrong" in any way.
The vagaries of the Fate Point economy just didn't work for us. Maybe we're broadly too traditional in our collective tastes, but it felt too often like you had to trawl for Compels to ensure you had FPs to use later on, rather than them "driving the story" or some such.
In my games, we end up with *maybe* 1-3 compels/session. I think the desire to always have "enough" Fate Points is often driven by the assumption that you should win every encounter.
Fate's not really like that so much. I tell my new Fate players that they should expect to lose frequently.
And Compels *should* "drive" the "story". A Compel should incur a significant enough cost that it *changes what happens*.
Furthermore, it seemed most tasks came down to whether or not you were willing to throw a load of FPs at them in order to guarantee a win.
This is absolutely correct. Moreover, it's *by design*. Fate isn't about "challenges" so much as it is about "dilemmas" and cost. The primary thing when encountering something isn't "is my build/skill enough to overcome this?" so much as it is "how much do I want this, and am I willing to pay the cost?" Sometimes that cost is Fate Points. Sometimes it's Consequences.
Refresh didn't work as a balancing mechanic. I remain completely unconvinced by it to this day. Far too often the powers were more useful than the FPs, or having them meant you needed them less.
Stunts/powers vs. Refresh is all about specialization vs. flexibility. I don't know your game, but if you're running a mostly-combat game, stunts/powers *will* vastly outshine refresh. The advantage of refresh and having high Fate Points is that you can use them outside of your "specialty".
The Skill pyramid/column just seemed arbitrary and neither realistic nor well-balanced as a means of allocating competence.
It's not realistic. I do find it reasonably effective as a balancing mechanism, especially if you're playing a game where all of the skills matter (that's one of the explicit guidelines in Fate Core, actually, that the skill list for a game should be a good indicator of what the game will be "about").
If you have a reasonably diverse table, it works. It also works better with players that have really grasped how much can be done with Create Advantage/Maneuver/Make an Assessment/etc. If all the players think they should Attack every turn, they're not really using their characters' skills effectively.