Do you need the gym to play football?
No. Plenty of people play football their whole lives without touching a weight, and they enjoy it.
The honest question is a narrower one: if you want to move up a level, or you want to still be playing in ten years, does what you do at the club cover it?
It does not, and that is not a criticism of your coach.
What a team session is built for
A squad has twenty players with different bodies, different positions, different injury histories and wildly different amounts of football behind them. One session has to work for all of them.
So it is built for the average. It has to be. And nobody is the average.
The session covers what the team needs: shape, patterns, fitness, the ball. It does not cover the fact that your left leg is measurably weaker than your right, that your hamstrings have never been trained at the speed a match takes you to, or that your calves have been quietly warning you since November.
Those are individual problems. A team session cannot solve individual problems, because it is not for one person.
The gap, specifically
Three things fall through it almost universally.
Maximum strength. Team training rarely produces enough force in one effort to build it. You need external load for that, and there is no external load on a pitch.
Top speed. Most amateur players never actually sprint in training. They run a lot, which is a different thing. A hamstring that has not been near top speed since pre-season meets match speed cold, and cold is where things tear.
Asymmetry and history. A leg that is weaker, a joint that has been injured, a tendon that grumbles. Nobody in a squad session is going to notice, and the session would not change if they did.
That gap is where injuries live. It is also where most of the improvement you are looking for is sitting.
Two hours a week
Two sessions closes most of it. Not five. Two, done properly, every week, for months.
That is roughly two hours out of a week you are already spending three or four on football. And it is the two hours that changes whether you are available in March.
What it is not
It is not five days a week. It is not training to failure. It is not a pump, and it is not the gym you see on Instagram.
Forty five minutes: something explosive first while you are fresh, two or three heavy lifts, then the specific things your body needs. Usually hamstrings and calves, because those are the two that get hurt and the two nobody trains.
Who should not bother
Worth saying, because this is not universal advice.
If you are under about thirteen, the gym is far less important than playing a lot of different sports and learning to move. If you are already training five times a week with a club, you have a scheduling problem rather than a volume problem. And if you are playing purely socially and enjoying it, none of this is a moral obligation.
For everyone in between, the honest position is this: the club session was never built for you, and two hours a week is what it costs to cover the rest.
If the answer is that you do want the gym, the next question is what actually goes in it. That is the exercise hierarchy.