It makes a lot of sense. You're ignoring what a realistic action and response would look like.
The goal wouldn't be to conquer large swathes of NATO territory. The goal would be to test the integrity of the NATO alliance, and to see if the Russian sympathizer sitting in the White House will renege on the US's obligations.
Imagine Putin sends a few hundred troops over the border and seizes a small amount of land. NATO is not going to use that as an excuse to launch a total war against Russia. Sure, if the full might of the Russian army comes storming into Poland, NATO would let loose everything we have. But a limited incursion like in Georgia? If NATO is living up to its promises, sufficient force would be deployed to drive them out. There would be no need to launch a total war.
This would be a way to test the NATO alliance at relatively low cost and risk. We don't actually know how Trump would respond to this. He could very well say, "not our problem" and refuse to render aid. If he did command the US military to defend NATO territory, then the cost to Russia would be small. A few hundred casualties in a war that's caused hundreds of thousands. A rounding error. A small price to pay.
But imagine what Putin gains if Trump doesn't offer assistance against even a small incursion. NATO's guarantees will have proven fruitless. Even if someone more friendly to NATO gets elected after Trump, the promise will still be broken. Every NATO member from then on knows that the NATO guarantees cannot be relied upon. A guarantee that is subject to the whims of which American political party is in power is not a guarantee that nations can rely on for their national defense.