Most countries have better things to do than perpetually going to war and meddling in the affairs of other countries. So on the contrary, there is no reason - inherent or otherwise - why Western Europe would get at all involved in this war. It’s a catastrophe for WE and by extension also for EE.

The US do have an interest and they’re dragging/pushing WE into the fire while EE are jumping head first with barely any encouragement.

If anything the EU has proven that the East-West rift cannot be overcome and that they do not have strategic independence.