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I see a lot of people with a grief for psychic powers, so I thought how you could redesign the system without adding too much complexity to make it more fair. This is a suggestion based largely on 6th edition Fantasy magic system, it's goals are two-fold: to make the better powers harder to use and to make the less good (typically witchfires and maledictions) easier or more rewarding.

The big thing with this system is, really, to determine how easy or hard each power should be to use. While I provide a guideline, some powers are just weak sauce even if they are noted by GW to be Warp Charge 2 and this system won't actually do anything to fix the powers that just aren't worth the ink they are printed with (looking at you, Mind War and Death Mission!) Sorry if the item examples list is a bit Eldar-centric.

The Psychic Test
A psychic test is a roll of 1D6 plus 1D6 for each Warp Charge spent casting the power. This test no longer have any relation with leadership what-so-ever and is not an ability test. Any items that previously interacted with a psychic test due to the tie-in with leadership, now have those functions defunct. This also means that a psycher's worth is no longer tied to his leadership value, meaning that meanial squad leaders can still be valuable as psychers. A psycher may spend any number of Warp Charge available to him on his psychic test to increase his chance of success.

Mastery Level
As previously, each psycher generates one Warp Charge per Mastery Level and gains an amount of powers equal to his Mastery Level. Mastery Level's psychic defence has been toned down somewhat to make Maledictions and Witchfires more meaningful.

Difficulty Class
Each power has an associated difficulty class. The goal for this difficulty class is to aim for powers to have roughly 5 in 6 chance of succeeding (which would be what you get from a level 10 psycher casting a WC1 power). A power is considered successful if his psychic test is equal or higher than the difficulty class, regardless if he perishes from perils of the warp or not. Examples:
Prescience (Divination Primaris) DC 4
Precognition (Divination #5) DC 3 (norm)
Flame Breath (Pyromancy Primaris) DC 2
Invisibility (Telepathy #5) DC 7
Hallucination (Telepathy #6) DC 6

As you can see, the norm is a class of 3. Warp Charge 2 powers expect you to use two warp charges to succeed and adds at least 3 to DC, but the cheap sorceror might want to use only 1. Witchfires and Maledictions typically enjoy a small discount when considering their projected costs, which is why a unit-crippling ability like Hallucination is still easier than Invisibility, it's just a lot likelier that the targeted unit has some sort of defence against psychic powers compared to a blessing.

Perils of the Warp
A psycher suffers a perils of the warp wound on any roll of double 1 or double 6. Using more Warp Charge to cast a power not only improves your chance of success, but also increases the potential of suffering a wound. A psycher can only suffer one perils wound per psychic test.

Defences and other modifiers
Deny the Witch is gone. Any references to this rule are obsolete and does nothing.
A psychic defence increases the difficulty of successfully casting a psychic power. This will typically affect the chance of landing a Malediction or Witchfire on an enemy unit, but some defences may also affect blessings. Here are a few examples of modifiers to the difficulty class, and these all stack, by the way:
Unit contain one or more rival psycher or Psychic Brotherhood: +2
Unit contains one or more rival psycher of higher Mastery Level: +1
Unit contains one or more Runic Weapon, Adamantium Will or similar special rule: +1
Psycher is within the effect of A Shadow In The Warp: +4
Psycher is trying to affect a unit containing Kharn: +10
Psycher is carrying a minor psychic aid (I have no examples of this): -1
Eldar Runes of Witnessing (one use only): -4
Eldar Runes of Warding (one use only, declared prior to enemy rolling the test): +4
Eldar Spirit Stone: +1 warp charge per turn

Very cool idea, having had time to think on it, there's a couple of points to bring up

1) To make the most of this system, choosing powers needs to be possible, and this system seems like it could balance them enough to where this is more feasible than the current system. A lot of work yes, but I think it'd be well worth it.

2) Saying its 1D6 plus 1D6 per warp charge to pass the difficulty class feels weird. Using more warp charges to make passing more likely isn't a bad idea, but it feels a bit odd. A more interesting direction might be giving every Psyker some sort of psychic skill (not mastery level) that is added to this roll to beat the difficulty class. You could then have it so Eldar Psykers do naturally have higher aptitude for casting spells than imperials. You're no longer using leadership for psychic tests so I feel like there needs to be some sort of interaction between the model and its psychic abilities beyond warp charges, This direction is much more complex and work-intensive though.

3) For some of these less favorable powers, you could take some influence from DnD and make it so spending more warp charges on a power buff it. Smite for example, could be Assault 2 +2 for each warp charge spent on the power. This way, spending 1 warp charge on it results in a meh effect. But spend 3 and then dropping 8 of those lightning bolts on a unit would be far more terrifying. Similarly spending another power to make something a big blast instead of a small, or dropping another template, or longer ranges, or rerolling, etc, the effects could be far more diverse and scale with investment. This way the difference between strong and weak Psykers is not only number of psychic powers and ability to cast them, but also the strength or range of these powers.

4) all of your listed modifiers make sense, but that's a really big list that will only grow larger as more armies are taken into account. It might be easier to classify certain effects into groups, and then have these groups be applied to all relevant weapons. So rather than a block of text saying that shadow of the warp adds a +4 to the roll, it's just damping (4) or runes of warding are shielding (4).

Personally, I'd love to see a unit with brotherhood of Psykers USR's skill at casting be tied to the number of models in the squad somehow, but that could just be me. Great job on the rules so far though, I can't wait to see how they develop and play.