Back in the 80s I used to judge the success of a Reagan initiative by how much the left screamed. The more they screamed, the more convinced I was that it was exactly what needed to be done.
The SDI program had them screaming pretty loud. That program is what won the cold war for us.
No doubt SDI contributed, but my vote goes to the effectiveness of the All Volunteer Military. I was on active duty from 76-84, and I saw how we improved year by year. My first two years in Germany were pretty rough. For example, the weekend before arriving at my first duty station in Germany (1/77), we had a race riot in our barracks, and an E-5 was locked in his wall locker and tossed out a second story window.
Combat arms units like mine were susceptible to soldiers lacking basic reading skills...it was a real challenge.
My last two years in Germany we had a new Battalion Commander, a grizzled veteran who was sure he was on his last tour. He went after malcontents and soldiers that could not be motivated. Higher HQs howled as we discharged over 10% of our 600 man battalion. The results were stupendous, and played a large role in turning a C-3 battalion into a C-1.