I think your assessment of the problems is essentially sound. But I'm not too keen on your solution.
Your proposal is a lot more complicated than the canonical system, and if implemented I suspect it would pigeonhole spellcasting characters. A wizard specialized in air can do many different things in any given scene, but a wizard specialized in interference and binds with foci granting free shifts of persistence is pushed to take the same approach in every fight.
I've actually put a lot of thought into preventing players from being pigeonholed. For example, that's why I make the pyramid system for specialties more strict. You literally can't specialize so hard that the above situation happens. To reach +3 Power and +3 Control in any one action, you would also need:
5 specialties in a second action
4 specialties in a third action
3 specialties in a fourth action
2 specialties in a fifth action
1 specialty in a sixth action
That's 10.5 Refresh there from evocation specialties alone, and you've got a pretty darn wide array of options. If you compare this to the NPC wizards in the book, the power levels should be pretty close.
As for the free shifts of persistence, I made them so easy to get because a lot of the time a spell that lasts only one turn is pointless. For example, if your shield lasts only one turn, your opponent can just attack another party member, and then your turn was mostly wasted. I also gave shifts of persistence because it'll be harder to create super-high Power blocks with the stricter pyramid system for specialties.
Also, the bonus for designing a focus exclusively for a single rote is implicitly stronger with these rules. Normally you'd only get an extra +1 power or +1 control. With this, you can get a whole extra +1 shift of persistence, worth +1 power AND +1 control (but not as flexible). This means that for one Focus slot, you can get +2 Persistence to a given rote. I did this to encourage players to take a wider variety of foci, rather than dumping all their points into a single focus and getting pigeonholed.
Furthermore, as another system to prevent players from being pigeonholed, I also made it so that cramming too many focus slots in a single focus costs extra.
PS: What do you mean when you say shields are "omni-directional"?
An omni-directional shield would cover you completely, rather than simply facing in one direction.
My approach to Foci was based on what Dresden says his Shield Bracelet lets him do. He mentions at some points that without his bracelet, he can only make a quarter-dome of force, but with the bracelet, he could create a complete dome of force for the same effort.
I also agree with your assessment. I like the approach you are using but I have to agree with Sanctaphrax that it seems overly complicated.
I've tried to 'fix' spellcasting but it's been mostly nerfing their foci. I like the idea of having foci focus on something other than power/control.
One of the big things I did with foci is limit the Total Power of ALL your foci to your lore. (not just each item)
So, if your lore is 4, all your evocation foci combined cannot be greater than 4. Each power has its own cap, so if you have thaumaturgy, you can have another 4 foci points. Then you can take foci specializations to increase your cap.
Anyways, it doesn't do much to change the flavour of wizards. You'd still max out your favorite element. All it does is keep numbers the same as everyone else.
I don't see any need to put the limit on all your foci combined. You can still only use one focus per spell, so all that does is limit the player's creativity and encourage them to min-max even harder.
Why have a shield bracelet when you can only use it for your shielding spell? Why not just dump all your focus points into a single offensive focus that handles the widest array of situations with the largest bonus?
If you want to "keep the numbers the same as everyone else", then just limit the maximum slots you can cram into a single focus. If someone decides to make a wider variety of foci anyway, it'll be a poor decision from a min-max perspective, but won't overpower them.
What if each element was better at a particular action? Like, each element can block/attack/maneuver/counterspell/veil but some are better than others.
Fire=attack
Air = maneuver
Earth = block
Water = counterspell
Spirit = veil
You're still better specializing in one element. For example, say Earth gives +1 Shift to Blocks. Which would you rather have:
+4 power/control for Fire
+2 Power/Control for Earth, and +2 Power/Control for Fire
The Fire specialist has +4 Shifts for Blocks, while the Earth/Fire generalist has only +3 shifts for Blocks. There's still no reason to mix your specializations.
Maybe buying a focus in a particular element is cheaper for drawing Power when using it for it's preferred action?
And/Or a focus slot is worth an extra bonus if it's for a specific rote (which stacks with the current rule for rote foci)
Something like that. So it encourages multiple foci to make spells cheaper cast for specific actions.
Foci already get an extra +1 when they're designed exclusively for a specific rote. What are you referring to?
Edit: what if foci give you armour against backlash for a specific action. So, in the above Fire example, you could overcast an attack spell, take two mental stress and, when you fail to control the extra shift of power, you soak it with armour. It lets you put more 'oomph' into a spell action without increasing accuracy.
So, it doesn't nerf anything, but it gives incentives to broaden your focus selection....meh
This would be hard to balance. Armor vs Backlash is the same as Control for most spells, but weaker for attacks. What do you charge for it? If you charge the same as an actual point of control, then it's overpriced and you should never take it. If you make it, say, half-price, then Backlash/Fallout lose their teeth as an interesting game mechanic.
I think you could actually blend the two ideas, Strill's and RaW, to great effect.
What is the difference between Specializations and Foci really? There isn't one, not fundamentally. They both adjust power and control for elements. They just do it differently.
Sanctaphrax's point is well made. You don't want to force pigeonholing on a character, but you can make it a strategic option.
So if specializations work the way Strill has outlined, representing a course of study or a proclivity for a certain type of spell that works across all elements (but dropping the ladder requirement), then foci can work as they traditionally have, boosting power and control for an element or number of elements. At this point, there is actually a choice to make.
A greater mind than my own would actually have to run through how these options might pan out, if there is any incentive to specialize.
The ladder requirement is specifically what prevents you from being pigeonholed. Otherwise, you just put all your points into attack, and use that to the exclusion of every other option.