How critical is it to have psi soldiers in my squad?

Solution 1:

You have to get extremely lucky to get a whole squad of PSI-powered soldiers. I tested quite a lot (30-40) of soldiers and I had maybe 5 that were gifted and 3 that survived and made it to the highest rank.

I like to bring at least 2 PSI-powered soldiers with me in every battle. The very high hit-chance of Mindfray can take out monsters when it really matters (team fires at monster, but it remains with some low HP). Or – even better – they can mind control an enemy, which can turn the battle in your favor instantly. Turning a berzerker Muton is one of the greatest things. Not only will it draw (and soak up) enemy fire, you can also go and kill stuff with it in the next turn.

Regarding PSI-skills to select: The defensive PSI-skills are good as well, but I have only used them once (to calm down a panicked soldier), whereas I use the offensive spells pretty extensively. I think smoke-grenades make for a better defensive tool most of the time.

So in summary: PSI-powered soldiers aren't critical to your squad, but they can broaden the number of tactics you can choose. The spells don't cost ammo and can be casted multiple times, which makes them a no-brainer. Mind-control is extremely powerful and can hit with a chance of 100% almost all the time with an experienced soldier that wears PSI-armor.

Solution 2:

Psi powers definitely aren't a prerequisite for winning the game, as long as you have at least 1 operative who is gifted for plot purposes, however, they are great. With 6 psi soldiers, you can use mindfray to have a guaranteed kill against 2 heavy floaters/elite mutons, 6 thin men/floaters, 3 regular mutons, etc.; provided you have LoS on them. PROTIP: use mindfray to soften up targets, as it decreases their will and other attributes - if one operative has an 87% chance to hit and the other a 100%, use the second's ability first and the first operative will have a 100% to hit.

Mind controlling an enemy can give you a chance to catch your breath, especially if the other aliens are closer to it than your soldiers, as they will have no hesitation to fill their ex-comrade with plasma. A nice bonus of mind controlling an enemy is that if it is killed while under the effects, its weapons will not self-destruct.

Panic can also be quite useful to disable flanking enemies or enemies that threaten one of your operatives. The lack of penalties for distance and cover makes them especially useful.

If you are not playing on Ironman, you can make all of your favorite operatives gifted.