I can’t tell you why it’s always on the right, but it’s always on the same side because of network effects.

Bicycle frames are not fully symmetric left-right because you need things like a mount point for the derailleur hanger, and optionally affordances to keep the chain off the stays when the wheel is removed.

Those things have to be on the same side as the chain. Bikes designed for disc brakes additionally need a mount point for the brake caliper on the opposite side from the chain.

Additionally, rear wheels are not symmetric: the spokes on the chain side connect to the hub closer to the plane of the rim. That is, they are more perpendicular to the wheel’s rotational axis than spokes on the opposite side (which is why you should always mount a single pannier on the chain side). This asymmetry is to provide space for the gears.

So once the industry decided to put the chain on the ride, you can’t very well make a group set designed for a left chain if you want it to work on the vast majority of frames.