Thought I'd update this since I happened to come across a 1993 Klein Owner's Manual that would appear to have the answer on head tube badges:
Page 19
"Effective November 1992, all frames shipped outside of the United States and Canada will have a head tube badge and other special markings. If frames without these head tube badges and other special markings are taken to dealers or distributors in foreign countries for warranty repair, the owner will be referred to the dealer he/she obtained it from."
A few mentioned that Markus Storck requested that head tube badges be put on the frames. This makes sense as perhaps Storck was trying to obtain repayment for warranty claims made on Klein frames in Europe and Klein disputed the claim by saying that it was a U.S. frame and denied the warranty. Putting head tube badges on a frame could help Storck's dealers/distributors know whether or not to honor a warranty claim with the customer. I don't know what their warranty was in Europe or elsewhere, but Klein offered a "lifetime warranty" in the U.S. However, there are many stories where customers made a warranty claim and Klein denied it citing "customer abuse" vs. a defect in manufacturing.
To me, these customer stories coupled with the info in the Owner's Manual, the content I've read here and elsewhere, and having worked 20 years in retail all lead me to believe that head badges "and other markings" were applied to non-US/Canadian frames in an effort for Klein to effectively handle its warranty claims.
Something like this perhaps:
There were many bikes that ended up in Europe but weren't sold through Storck and the European Klein dealer network. Ultimately some of those bikes would need servicing under warranty. Most Euro dealers would probably take the broken bike frame from the angry customer and exchange it on the spot for one they had in stock. The dealer would then send the defective Klein frame to Storck, or directly to Klein, and file a warranty claim with Klein expecting to be reimbursed since the dealer had already given the customer a frame from his existing stock. Klein would receive these defective frames and probably noticed from the serial numbers that some of these were U.S frames. "Why are we getting defective U.S. frames from our European dealers? Warranty Denied!!" A small Euro bike dealer can't be expected to look at a Klein frame and know just from the serial number whether it's a U.S. or European frame and whether it would qualify for Klein's warranty reimbursement. You can also imagine the European dealers complaining that Klein wasn't reimbursing them because a U.S. frame didn't qualify under the terms of their European warranty. So the solution would appear to be that Klein started making it much easier for their dealers & distributors to identify a non-U.S. frame from the head tube badge and other special markings. If the frame had these items, then the dealer would know whether or not the customer had the bike shipped directly from the U.S. (gray market) or if the bike had come through the proper European distributor/dealer network channel.
Long winded but hopefully helpful to explain the "why" behind them applying these badges but at least we have that November 1992 is the official time that Klein says they started doing it.