A slight "tilting" of the clutch plate - as I understand what you're doing - would be normal - there has to be some play or you'd be at severe risk of binding. 3mm at the outside of something the size of the clutch disk doesn't sound particularly excessive.
Looking at my own 130,000km input shaft and another one beside it with less, there is NO taper of the splines, nor should there be. My splines measure out at 23.51mm max dia. - at both ends of the splines - 0 taper. That's at 130,000km.
(Gerd, for your information - your "teeth" in this case are technically called "splines" but "teeth" is understandable. Splines are finer/smaller than teeth and are used in this design of a shaft into clutch, whereas teeth are on the gears in the transmission and mate with another gear)
The input shaft spline wear is a well-documented and frequent problem. The splines should be greased with a good anti-seize about every 25,000 miles or less.
>>100km (is that km or miles - don't know where you're from - click on "profile" to fill that in)
If there is tapering, or any sign of wear on the splines, it's time to replace the shaft.
Also, replace all the ball-bearings. The roller bearing on the input is probably fine for a long time, but the ball bearings have been known to fail with regularity. Mine did recently at 100,000km on it. Many mechanics figure that it's a "regular maintenance" job to replace the bearings and inspect every 100,000km or 60,000 miles for normal use. Then someone will come along and tell you that's nonsense, they got 250,000 on theirs and it's still fine. Always someone who breaks the rules and gets away with it!
I'm very easy on my gearbox, smooth shifting and I don't lug it etc, replace oil at every service, and it still blew the large ball-bearing spectacularly, wiping out almost everything. Sad - the gear dogs were almost like new, no significant wear at all - but the teeth were chewed up by the shrapnel circulating. The splines are still perfect, but they were lubed at 25,000km intervals. The clutch is perfect, less than half-worn. In fact I find it amazing that people carry spare clutch plates as long as they know to look at their splines and lube them occasionally.
Hope that helps,
One world, Two wheels.