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To support your point here, here is a list of some international wars since the end of WW2 in which a dictator invaded another country but they failed to get more out of the war than a stalemate:
The Korean War: North Korea invaded South Korea, but after interventions by both UN forces (led by the US) and China, the war got bogged down on a front line close to the original border between North and South Korea. There were no signs of instability in either of the two Korean governments, and no nuclear weapons were used despite the US being in unilateral possession of them at the time.
Soviet-Afghan War: The USSR invaded and set up a satellite state in Afghanistan. After a decade of fighting a protracted guerrilla war with insurgents backed by the US, the USSR withdrew from Afghanistan in 1989, just before the collapse of the USSR. It has been suggested that the defeat in Afghanistan played a part in the dissolution of the USSR, but it seems like it was far from the decisive influence to me. We can count this as a partial success for Tegmark’s thesis at best.
The Iran-Iraq War: Saddam Hussein invaded Iran, but the war became a stalemate that lasted for eight years before status quo ante bellum was restored. There was no sign of instability in his rule that I’m aware of as a result of this debacle.
The Gulf War: Saddam Hussein invaded and took over Kuwait, but subsequently got kicked out of the country by coalition forces led by the US. The US also encouraged rebellions throughout Iraq against Saddam’s rule. These rebellions were crushed by Saddam’s government following peace with the US and its allies.
While the sample size is small, and my memory here may be biased, I think the outside view evidence certainly casts doubt on Tegmark’s thesis. Unless we have some very specific inside view reasons to believe Putin would be overthrown in the case of agreeing to something resembling status quo ante bellum, which I don’t see, Tegmark’s assessment of the odds of Putin being forced from power in such an eventuality seems overconfident.