I would say that the burden of proof is yours first.
But since you asked...
> The church as an institution certainly prefers the more radical conservatives as you go higher up the chain
Where are these "radical conservative" bishops? They're anything but "radical". If anything, they tend toward a soft middle that is very slow to act. Indeed, that's one of the gripes "radtrad" types tend to have. They would prefer more bishops were made in their own image.
Instead, we see bishops aggressively curtailing more traditional expressions of the faith, while permitting plenty of liturgical abuse of, shall we say, a decidedly "untraditional" stripe.
> So in the long term they will only be left with a bunch of crazy radicalists and a silent majority that wants absolutely nothing to do with them.
You can't be serious. If anything characterizes the post-Vatican II Church, it has been the greater influence of "progressive" and "modernist" elements, some of them quite radical. Only in relatively recent times are we seeing a growing, younger crop returning to traditional forms. You can expect that the Church will look more traditional within a generation or two.
Your claim reminds me of those who clamored to make the Church more "relevant". They claimed that if the Church didn't do so, it would lose the youth and imperil the future of the Church.
Instead, what we saw was the reverse. As the Church became more "relevant" - which is to say, more concerned with the temporal and the temporary, conforming to the times instead of shaping men and the times - it became less appealing to the youth. It should be obvious in retrospect. What people desire from the Church is the eternal and the transcendent, not more of the same that you can get elsewhere and in bulk.
So, all that "relevance" produces is a large exit of the youth from the Church. Attend a "progressive" parish and you'll see plenty of empty pews with a few aging boomers. Go to a more traditional parish, and you see the pews brimming with families. These are not isolated cases. These are broad trends.
If you do see a swing toward the traditional, it is not because "crazy radicalist conservative" bishops are concentrating those elements, but because of a process of natural selection. "Relevance", it turns out, is dysgenic. And as the traditional element increases and becomes more visible, so does the visibility of its substance, which is what attracts converts and reverts.