So everything ends up on the same footing as rest mass?

At zero velocity, it has only its rest mass energy-notuseful for our purposes.

This is true even for photons, which do not have any rest mass at all.

This particle's rest mass is much lower than that.

When they collided, this kinetic energy could be converted to rest mass energy, so that particles of higher mass could be created.

Each one has its own distinctive rest mass which serves conveniently to identify it, though there are also other, more subtle, differences.

Stick to photons -no resting mass, no charge, no controversy on the human scale.