almost all starters now days don't require the shim. it would be rare for the shim to completely cause the starter to miss the flywheel. they will sound weird, and eventually cause damage if they need one, and it isn't there.
here's the 100% diagnosis of a starter. when it won't engage, have someone crank it, and then someone else hit it with a hammer, if it works when hit, get new starter.
hillbilly technology still used today. never fails