There is no single way to go about playing the game There are strategies that accommodate many different play styles.
The reason you stick with a single chassis normally is so when coordinating with teammates, you minimize your losses (also why people tell you to build concussive armor only). If you have an enemy with tanks splitting between 10 anti inf, 10 anti veh and 10 anti tank and you send 10 infantry, 10 vehicle and 10 tanks to fight it, you are maximizing your losses because each anti chassis type is dealing full damage.
Concussive will always hit infantry first
Beam will always hit vehicles first
Explosive will always hit tank first.
Concussive does 100% dmg to infantry. 50% to vehicle. 25% to tank.
Beam does 100% dmg to vehicle. 50% to tank. 25% to inf.
Explosive does 100% dmg to tank. 50% to inf. 25% to veh.
If you ONLY have vehicle units attacking however, then the beam will do 100% dmg, the explosive 25% and the concussive 50%. Meaning, overall you minimized damages.
Now, of course, there are downsides as well. As you continue fighting through the era, other teams will notice what you are making and make anti chassis accordingly. So if you were infantry, potential enemies will likely make concussive infantry squads to fight you. And say you're fighting an enemy with vehicles, so your armies are mainly beam. Now when the other enemy comes to hit you, you are at the absolute worst situation. You have infantry with a focus on beam (25% dmg to inf) and they are infantry with a focus against infantry (100% dmg). In this situation, having someone with a different chassis could be your saving grace. Especially if it's concussive focused tanks.
If you are looking to hit from different fronts on an enemy (if say, you have 3 members on a different side of map and you are sandwiching your enemy) then having 2 different chassis types can be advantageous as they will need to build anti for both. However, this of course means they don't have to build as much for either at the same time. It's a common tactic for teams to use subs that build at their weakest point to cover. For instance, a main alliance goes tanks. They'll assign their sub to go vehicles so that if a team focus's heavily on explosive, their sub can counter.