Perhaps we didn't realize how much stability the "two powers" model generated. It caused inevitable arms races as the two powers vied to stay competitive, but there were only two. And the USSR was able to de-escalate on its own. If you have three powers, each of them wants the ability to eliminate not one, but both of the others. Could lead to not just incremental, but polynomial expansion of forces. And de-escalation involves multiple parties coordinating, not just one great power.