TLDR : Infiltrators are not practical (kinda underpowered) for winning but are fun to play as. They could be removed from the game because the roles of combat and support are already covered much better by other classes...

What would the gameplay balance be like if infiltrators were removed from the game?

It feels like it wouldn't be very different.

How big would the playerbase be if this happened?

Removing Support would be horrible, no ammo or vehicle repair.

Losing Medic would make a impact, faster battles probably, would this be bad or good?

Losing Light Assault would take away a lot of the positioning freedom it gives. I think everyone likes the light assault?

Removing heavies... idk how this would work. On one hand, they offer contrast as a selfish unit that focuses on being a tank menace at the expense of less supporting. They seem very balanced to me.

On the other hand they are very simple, we already have maxes for the juggernaut role too. Maybe we would see more maxes?

Removing infiltrator.... idk if anything really changes much.

Infiltrators hardly give support, and their stats like speed and health aren't special. They just kill infantry in a slightly different way. I don't even think they have a faster kill rate.

Their hacking terminals is nifty assuming they even pull it off in the first place, but its more of a minor temporary annoyance. Kill him, fix terminal and move on with your life.

They could probably just give the a ability to Light assault or support too if we couldn't live without it.

While medics constantly revive and supports constantly ammo and repair for potentially massive consistent benefits...

The support from a infiltrator feels less important and more gimicky fun for the player, not the team.

While the infiltrators combat power isn't especially great either, it's fun for the player, it FEELS OP to the victims... but it probably isn't as deadly as a heavy or Light assault is in the LONG RUN.