The approach of the Catholic church is internally consistent, because it is premised on the existence of divine law which the church as an institution is specially entrusted with conveying to the laity.
That approach makes no sense in a secular democracy. There is no divine law to interpret, and there is no body like the Catholic church charged with mediating between divine law and the laity. The only source of authority is the consent of the governed. The constitution and amendments reflects the consent of a supermajority that can bind subsequent majorities. But any intermediate majority can be overruled by a subsequent majority. In that framework, the only sources of authority that can overrule the present majority are the edicts previously sanctioned by supermajorities. And the only relevant meaning of those edicts is what they would have meant to the people who consented to them.
If you dispense with the idea that the intent of the framers matters, then you’re dispensing with the authority of the supermajority that consented to what the framers wrote. That leaves only the present majority as the only source of authority.