I think there's some sort of misconception about EVM not showing schedule variances.
A good EVM structure should have sufficient granularity that a single late task should be clearly evident. That, coupled with a decent critical path analysis will flag problems with 1 week of discovery.
You cannot use the total rollup on a $15 million program to find small problems. By the time they show up in earned schedule OR earned value at the summary line, it's already too late.
A typical, perhaps overboard, example is where Lockheed Martin, ran EV on all tasks, with no task larger than 80 manhours. While a bit excessive, no single problem would escape notice by more than 1 week.
TTFN