Biggest problem doing only single reps is that if you are truly maxing out a single every workout that's quite a bit of cns overload and you will reach a point where you won't improve due to cns fatigue.
Do both full squats for overall strength development and half or quarter squats for speed in specific strength development.
If not the squat for runners then what? Lunge?...If you are going to lunge then you should squat to develop the lunge.
Peroidize your lifting like any other sort of training.
Looking just at the squat (i will assume the squat is part of a balanced strength training program) lets talk about progression. The squat, the lunge, and their variations should be the foundation of your strength program. Start with bodyweight movements. Do the full range squat. Go for reps and speed. Do timed sets and go for more reps per minute. Do numbered reps and sets and go for a higher number. Do this 2-3 times a week for 4-6 weeks (assuming you are also doing other bodyweight exercises).
Now move into weight training. Do 5 sets of 5 increasing the weight each set such as 95, 115, 135, 155, 185. You will learn by trial and error but start light and add weight until you reach failure at 4-6 reps. On those light sets lift more explosively but not jerking or jumping...down controlled, explode up but in control. Lift 1-2 x week.
After 4-6 weeks switch to 4-6 sets of 2-3 reps. Same protocol but a higher weight. Do this for 2-4 weeks.
Now switch to more dynamic and specific strength. If two days a week do explosive/specific lifts one day then plyos second day. If one day a week do combined but with less volume.
Explosive:
Quarter to half squat (135-90 degree knee) perferably to a box so you know the depth. Do 50% of the final weight you used last phase. Go for speed. 5-10 reps. 2-3 sets.
Specific:
Bulgarian lunges or walking lunges with dumbells. 10 reps each leg or walk for distance.
Plyos: basIc flat frog jumps and splIt jumps progress to box jumps for height and split box jumps (3 sets of 3). Also broad jumps and split jumps for distance. Choose two of these. Progress. Change exercise. Progress.
Trouble with squat....
Do heavy squats from pins. If you have a full cage squat rack set the pins at 135 degree knee angle...or use the smith if you really really have to. You should be able to do much heavier weight.. again 5 x 5. Also drop the weight in half from your orIgInal 5 rep weIght and do speed squats from a box. Set a box at your full depth (12in plyo box?). Squat down. Sit on box. Explode up. Weak from bottom use low box squats light weight. Get out of hole then stuck use heavy heavy squats from a high pin.
Plyos help your running. Specific and explosive strength helps your plyos. General strength helps your specific and explosive strength. I can't stand picking up a running book and seeing half squat cable pulls with an opposIng knee raise and some PhD calls that "functional" meanwhile those "athletes" can't do a full range of motion squat without getting up on their toes, they can't squat their body weight, and wonder why they have femoral neck stress fractures.
One of these days I will write a free book and offer it here...3 people will use it, 100 trolls will disect and ridicule it, 20 personal traIners/strength coaches wIll tell me It's not functIonal enough, 10 PhD's (who have never actually traIned anyone)will question the science, and some dude from TNFmedia will use it as a beer coaster. :-)
Alan