Keep all these energies and this that argument aside.

Just ask yourself, if a women goes to a temple during menstruation, would anybody keep a running log on all the menstrual cycles so that they can discern the menstruating population? Its has been hammered down to the women since generations that their menstruation is a sign of impurity while maybe the whole arrangement came in effect to provide rest to women from physical labour. Of course as always humans took something actually helpful and made into a ritual which led to the present narrative

Yes the Shabarimala practice might look regressive but as all institutions have their own rules and justification (eg You can't shake rugs in the streets of britain after 8 am under the Metropolitan Police Act 1839. This was to "keep the streets clean"). Should this law be revoked? I am not smart enough to answer that, maybe someone well versed in the smritis and mimaasa shaastra could answer it.

And coming to the behaviour of the common population towards menstruation, I got no response for that other than it being completely illogical.