All of Eastern Europe would disagree with you.
Reagan did bring down the Soviet Empire, and it was not détente that was practiced before him, it was appeasement and fear. Many on the left in this country thought the Soviets had a system of government that was admirable and ours contemptible. Just look at the current Cuban apologists and the anti-war movement.
Reagan turned that all around. He supported a massive military buildup, Solidarity, the afghan war, contra rebels, missiles in Europe, Granada, etc., all opposed by many in the dem controlled congress. That is not détente. That is war by other means.
Nixon's best-selling book, The Real War, which was published just before the first Reagan presidency, dealt, in part, with what the U.S. response should be in the event the Soviets 'cheated' on the agreements reached during detente (in the Nixon-Brezhnev summits), and Reagan implimented the U.S. response (the stick: increased military spending), BUT in the course of his summits with Gorbachev he also stressed, at Reykjavic, the carrot (disarmament) -- so distressing to many U.S. (and European) conservatives. The fact that this strategy worked so well with the Soviets is the reason it is now being pursued with China.
The impeccable credentials of Nixon and Reagan as hardline anti-Communist Cold Warriors were what made the pursuit of detente with China and the Soviets possible. It is seldom mentioned that, prior to Nixon's first presidency, there were no meaningful negotiations between the U.S. and the major Communist powers. Dulles and Ike made tentative moves in that direction, but never succeeded, and, in spite of their best efforts, JFK and LBJ failed miserably because they were unable to project U.S. power as Nixon and Reagan could: JFK's one meeting with Khruschev in Vienna led to wrenching crises in Berlin and Cuba, and LBJ's meeting with Kosygin in Glassboro was a dud.
In brief, because even their political opposites in the U.S. trusted Nixon and Reagan would not sell out U.S. interests, they had no misgivings about allowing them to engage in high-level negotiations with the Soviets and China. And because the Communists knew they were dealing with anti-Communist hardliners, they knew it is was in their own best interests, in Churchill's famous phrase, "to jaw, jaw, jaw rather than war, war, war." To wit, summitry, the agency of detente, was a viable modus operandi under Nixon and Reagan. Ironically, the fruits of the labours of the two most important U.S. architects (there were European contributors of course: Willie Brandt, Helmut Schmidt) were gone before success in eastern Europe was realized under Bush I.