Why Doesn't the House of Representatives Dominate Our Government?

Mr. Wilson, August 13, 1787:

In Convention: He did not mean to enlarge on a subject which had been so much canvassed, but would remark as an insuperable objection against the proposed restriction of money bills to the House of Representatives that it would be a source of perpetual contentions.... The President here could not like the Executive Magistrate in England interpose by a prorogation, or dissolution.... The House of Representatives will insert other things in money bills, and by making them conditions of each other, destroy the deliberative liberty of the Senate.

He stated the case of a Preamble to a money bill sent up by the House of Commons in the reign of Queen Anne... in which the conduct of the displaced Ministry who were to be impeached before the Lords was condemned; the Commons thus extorting a premature judgment without any hearing of the Parties to be tried, and the House of Lords being thus reduced to the poor & disgraceful expedient of opposing to the authority of a law a protest on their Journals against its being drawn into precedent...

Indeed. It is a mystery to me why no Speaker of the House ever laid down the principle that the House does not assent to any amendments to its money bills, but simply repasses the bill in its original form. And once any Speaker has established that principle, it is the House where all the action is.