This was literally the theory that guided European (and particularly German) relations with Russia for the past couple decades. It was disastrously wrong.
Russia knew that the consequence of launching a war would be the evaporation of trade with Europe, and they still did it. They won't attack NATO because it's NATO, with overwhelming nuclear and conventional military forces, it has nothing to do with trade.
It's a fallacy to focus on the one failure of the policy and ignore the other cases when it was working.
As for NATO its expansion all the way to the borders of Russia didn't prevent the war either, and it remains to be seen whether we won't end up with a war between Russia and NATO.
In times of war it's tempting but dangerous to feel like militarisation of the world is the solution. History doesn't show that to be the case in general.
The mistake is on believing that the effect was symmetric. Russia benefited very little from the trade (yes, for internal reasons), so they made no effort to preserve it.