Can't imagine anyone would object to that smart idea :)
I wouldn't really object if the government knew when I cycled into town, and when I visited friends etc... if it would get my stolen bike back. There could also be a rule that only bikes reported stolen could be logged and alerted, but there could also be benefits if this rule was let slide. For example, popular cycling routes could be studied for prioritising path repairs, or the building of new cycle lanes.
And your 90% estimate is as offensive as wrong.
I doubt the thieves go to so much trouble, though, I expect my bikes that got stolen -- happened a few times -- ended up resold in the same city or in a neighbouring town. Wouldn't be totally shocked to recognize my own (well, formerly) bike in the local classifieds.
Also there are actually two types of bicycle thiefs: organised groups that load them by the truckload and opportunistic folks that know most locks are trivially broken and just want a cheap ride. You'd be surprised how many times I witnessed guys just carelessly dropping "their" bike once arrived.