One reason why that is probably not true is because there are less positrons but if it were true they should number the same as electrons, right?
But if electrons are moving along the same "time direction" as we are and positrons are moving in the opposite "direction" then wouldn't we expect there to be less protons? As we can't measure the protons that already "passed" us? And we would measure more electrons as a some/many/all of the existing electrons are traveling alongside us?
Positrons are different from protons. Both have a positive charge, but a positron is an elementary particle of a similar mass as an electron. They are rather rare in nature which OP was noting. Protons are made of three elementary particles, much heavier than positrons, and are, I imagine, present in nature in about the same order of magnitude as electrons.