I won't suggest they didn't, but I'm also going to say the Eastern flank countries are pulling their weight. As a percentage of GDP, Poland is spending nearly double the US the last time I checked. No one is laughing at the will to fight or the budgets in the Baltic nations.
With all that said, Europe is waking up and they are increasing spending. Also, those rotational forces are aided throughout the flank by the rest of Europe and even a rotational Canadian force - I know you might laugh at it - but the numbers are not insignificant.
I find it hard to believe the Army is stretched thin doing legitimate training exercises in a place that is reasonably likely that war could break out but you obviously would know better than I.
Edit: I see you talked about the numbers of the Army there and I get the strain, but it still doesn't address the issue that bases in Europe have, do, and will continue to provide strategically important basing locations for us to project power outside of Europe.