To break this down a bit:

" intervention early on, in Eastern Europe, would have made others think twice before moving forward"

This is definitely something Eastern European communist leaders argued to Gorbachev. He refused to provide military support to back up their regimes. The reason was, in short, that he was serious about ending Cold War tensions in order to focus on reforming the Soviet economy (in a roughly democratic socialist sort of way, I should emphasize). He knew the sort of international outrage that had come from the invasion of Hungary in 1956 and Czechoslovakia in 1968, and was unwilling to go that route again. He basically urged members of the Warsaw Pact to pursue reforms along the line of perestroika and glasnost - and Hungary was doing something similar already at the time. He seems to have been genuinely surprised that the communist regimes there were so swiftly and utterly rejected - but again, he wasn't going to risk large scale military interventions to change that.

As for the "Parade of Sovereignties", that specifically was about Soviet Socialist Republics and other autonomous areas declaring "sovereignty" within the USSR, with an especially big rush of such declarations in 1990. As I describe in an earlier answer I wrote here, these declarations were part of a protracted renegotiation of the constitutional order that Gorbachev undertook starting in 1988. They were as much bargaining positions as outright declarations of independence, and a big chunk of early 1991 was spent between Gorbachev and the republic heads negotiating just what all this would actually mean.

During that time, the Soviet military did intervene against independence-minded forces that they deemed had gone too far. Pro-independence protests were repressed by local Soviet military forces in Tbilisi, Georgia in April 1989 (with hundreds of casualties). Riots in Baku in January 1990 led members of the non-communist Popular Front to barricade the city, resulting in a Soviet military crackdown there that killed hundreds. Independence movements in Latvia and Lithuania led to the economic blockade of the latter in 1990, and the "January events" in both countries' capitals. The Vilnius events involved Soviet Airborne Troops and most notoriously involved an attack on the Vilnius TV tower, were 13 people were killed.

Ultimately these attempts backfired immensely - the repression and loss of life if anything increased local support for independence movements from the USSR. They also not only undermined Gorbachev's political capital, as a peacemaker and as a trustworthy leader, but also undermined his support in the Soviet military and security structures themselves. They felt they had undertaken such actions with his approval, but in the case of the January 1991 events in particular he distanced himself from these actions once they became liabilities.

A much stronger military intervention maybe could have crushed independence movements and public unrest in the USSR in 1990-1991. But it probably would have required a leader with Stalin's ruthlessness, and no doubt would have involved long counterinsurgency campaigns (has had been required after the annexation of the Baltics and western Ukraine after World War II). This wasn't the kind of leader Gorbachev was, and even the Soviet leadership that opposed him in the August 1991 coup was one that had initially supported his structural reforms - they were trying to stop him from going further, but owed their positions to the reforms he had done to date and were "locked in" to the current order, and unable to turn the clock back.

Such a crackdown would also have attracted massive international outcry, increased isolation at a time that the Soviet economy was also unravelling with steeply rising inflation and falling official output, and been very much at odds with the kind of society that Gorbachev and the rest of the Soviet leadership had been promising to its people. It's possible it could have been done (North Korea pulled off something like this with "only" suffering a massive famine in the early 1990s), but it would have been extremely hard.