Although this is a viewpoint claimed by many Protestants, Catholics would say that there was never a difference between Protestants and Catholics in a view of scripture as the final authority. The difference (this is a crude simplification of some very complex issues)was rather between private interpretation (protestant) vs. ecclesial interpretation - the triad of scripture, tradition and reason (catholic/orthodox).
Hooker's so-called 3 legged stool (or triad as you called it) was never that. (It is claimed to be by a lot by revisionists in Anglican circles now though, actually). I've read the quote where that idea came from, and clearly Hooker saw a priority...with scripture as the final authority, reason as secondary, and tradition in third place. This view arguably was also held by the Reformers...and is not a contradiction to their understanding of sola scriptura (which refered in 16th Century minds as final, unarguable authority, not solo authority).
Magisterial/Confessional protestants (Lutherans, Presbyterians/Reformed, and Anglicans) have always maintained it was the Church which had the responsibility of interpretation--hence the various confessions--hammered out and agreed to by highly qualified scholars in the church (not private interpretation)--which explain and detail what they aggreed in community as biblical doctrine.
I've recently taken a seminary course in Creeds, and it is fascinating how very much the historic Protestant creeds agree on...probably upwards of 95% between Lutheran and Reformed, and 98%+ between the various (many) Reformed creeds.
Me-and-my-Bible-alone Christianity is pretty well uniquely an American phenomina, and has been (and continues to be) on the fringes of Christianity--even Protestant Christianity. Even those groups (take Baptists for example) who claim to follow it....really don't tolerate private interpretation very far at all, their doctrines are developed (and interpreted) by their church scholars acting in community as well.
Let a bible study in a baptist church say they've come to understand the bible alows infant baptism....and those who say that won't be in their baptist church very long! So private interpretation of any great consequence in practice is very rarely tolerated by any group.
One of the wonders of all the various splintered Protestant groups, among the evangelical brand anyway, is the remarkable uniformity of belief--among groups who have no connection to each other in any sort of formal way.