I donít think there is a THE reason, as changing almost any of the variables may well have eliminated the problem. However, tire pressure is probably the easiest one to change and thus I would consider it the primary issue as it is the one that could have most easily been changed to avoid the problem.
Springs and shocks are very unlikely to be a factor in a high speed wobble. The suspension is hardly ever moving much until things get really ugly. The issue is a resonance between the tire, wheel, fork, and frame due to their flexibility.
I have not had any noticeable instability with my KLR either, but I have had it only up to 70 or so. However, the flex in the forks and chassis is very pronounced compared to my BMW. If I do a quick swerve on the KLR, I get oscillations at both the start of the swerve and the recovery that are very unnerving. My LT on the other hand, is rock solid. It enters a swerve and exits a swerve with no noticeable oscillation at the transitions. It simply goes where it is pointed. However, it has a large casting for the main frame and the Hossack style front suspension is very rigid. And the cast wheels are more rigid than spoked wheels, so it is no surprise that it is far, far more solid during high speed transitions as compared to the KLR.
I'm familiar with other bikes; I've had 41 so far. I still say the suspension, setup and loading are more likely "primarey" causes than tires or spindly forks but I concur that a number of "weak links" add together to manifest the problem and I agree that I would start on this particular bike by changing the tires and increasing pressure to try to reduce the effect.
FWIW, my standard wobble post:
Way too many people think that addressing the symptoms by dealing with handguards, fenders, fork braces, etc. are the answer rather than dealing with the real issue which is related to suspension setup and loading. I'm not convinced that the KLR is any more susceptible to instability than any other bike with long travel, lightly damped suspension and the Owner's have a propensity for severe and uneven loading.
There are some problems that need to be checked;
- bad/lose head bearings
- condition of wheel bearings and suspension bushings
- wheel and tire condition and appropriate tire pressures.
.....beyond that, It's settings;
- proper sag settings and adequate damping
- proper bike loading
- avoiding inappropriately un-aerodynamic loads
addressing the symptoms rather than the cause can help but IMO shouldn't be done until all the aforementioned items are checked and corrected if necessary. Nonetheless these can help stability;
- fork brace
- smaller fender or lowered fender (I use a polisport as I hate both the supermoto and low mounted fenders)
- consider tank bags instead of putting everything in huge panniers which affects both weight loading and aerodynamics.
My 2001 had some high speed issues that went away as soon as the sag was set properly....and after my Cogent suspension was installed, both my KLR's have been rock steady.....even with full knobbies and low tire pressures (20 - 22PSI). Lastly, as others have mentioned, the rider also plays a part; keep a relaxed light grip on the bars and don't tighten up. Changing your position (move forward/lean forward) can help too.