A near-guarantee that you'll be able to get off Invisibility or Perfect Timing or Iron Arm or whatever on exactly who needs it whenever they need it (and when you take Tigirius, the rerolls to select powers mean you have an additional chance to get that clutch power you were looking for). It means that enemies cannot shut down your key, clutch psychic power(s) (especially your Blessings, which are the best powers, since nearly every DTW bonus is only for when you are targetted) even if they're bringing 20 deny dice to the table, like the summoniest daemon psyker-spam possible that's out there. Plus you can throw a few dice at it and be practically guaranteed to get multiple successes, rather than the "oh yeah I threw 6 dice at this high ML spell and still failed/perilsed."
Essentially: reliability. The psychic phase has been the most random and uncontrollable phase for as long as it's been its own distinct thing, due to how few dice you roll in it and how important each of those dice are for it (compared to the dozens you roll for each squad in shooting or combat)--this virtually eliminates anything except the wierdest flukey bullshit, unless you get super screwed on power generation (which, again, Tigurius really helps mitigate).
The thing about psychic powers is that they are an asymmetrical gamble. Which ones you generate, which ones you actually manage to cast... if every one of your 3 Daemon Princes rolls Iron Arm, then you've basically won the game right there. If you have 2 or 3 Invisibilities in your list, you've basically won right there (barring an ITC FAQ). Some powers are extremely powerful, while others are... quite mediocre. Then you're at the mercy of the dice to cast, then not to get denied, then to hit (with witchfires like Psychic Shriek especially), then to actually deal damage... shooting only has to deal with half as many points of failure, and is usually easier to correct for (high BS, twin-linked, markerlights, orders, whatever). Investing in psychic powers is a risk at every level, but can pay off with exorbitant rewards when it hits. A Conclave eliminates much of that risk and softens the risk in other ways (not only do you basically auto-cast, but you ALSO are paying for a bunch of chances to get the power you want).
To say nothing of the anti-psychic potential that many MLs and psychic hoods can bring to the table. It really bothers me that far and away the best anti-psychic strategy in 40k... is to bring *more* of your own psychic than they have brought. "Perils on any doubles" that DE and Khorne can get, or bonuses on DTW rolls... really don't compare well to the sheer mass of deny dice that a list with a lot of psykers (like, say, a Conclave's-worth) can bring to bear--especially when psykers bring their own DTW bonuses to the table!