"Let them be neither" does not work, as demonstrated by the NATO expansion.
Germany for example has very strong economic interests with both the US & Russia, and until the Ukrainian invasion there wasn't too much of a problem with that. The US warned that Russia would use its fossil fuel exports as a political weapon (as it turns out, correctly, but the US wields economic influence in similar, if more subtle ways) but Germany was still free to enter into an agreement despite that, and it did so, along with many other European countries to a lesser extent.
Finland & Sweden were perfectly content to "be neither" for three quarters of a century! But now, faced with a belligerent Russian regime, they're driven to the extreme of knowing they could be next on Russia's list. Russia has brought this on itself, and if more countries are choosing a closer alliance to the west it is in no way through pressure or threats of violence by the west (or the US in particular) but instead due to fear of violence from a their neighbor to the east. Russia has created a situation where "we don't need to pick a side, we can be neither" is now a choice that risks annihilation of national sovereignty.
Ukraine got on the bad side of Russia because it was trying to do just that. It gained leadership that was willing to develop stronger ties with the West and Russia perceived it as a threat, annexing Crimea as stage-1 in their plan to eliminate Ukrainian sovereignty.
Instead they might simply have played nice, continue being the region's key supplier of natural gas/oil/etc., Used those proceeds to develop other areas of it's economy... You get the idea. Their leadership's nostalgia for empire building is, ironically, getting in the way of them building an economic empire. Their scientific tradition should have them at the forefront of new breakthroughs alongside other large nations. Instead, we get a fruitless invasion and another generation of isolation.
"Continue being the region's key supplier of natural gas/oil/etc" is not enough for Russia.