I'm not a tiler (just done 1st serious DIY job), but how about an engineer's view of blade wobble. I have the Vitrex pro 750 cutter as in Timeless John's photo above, for its quiet direct drive motor, larger than average table, quick release fence, and price. On 1st switching on, guess what, loads of wobble. It seems many would send it straight back, but a little investigation seemed easier. The blade's drive washer is clamped against a small shoulder on the drive shaft. We can be sure that the machining of the shaft will ensure the shoulder is exactly square to the shaft axis. But it is immediately obvious that the shoulder is too small (around 1.5mm I recall) to provide positive location of the washer. How much wobble you get is going to be down to luck. So 1st step was make sure there is no grit/gunge/rust on the shoulder or washer. Then pop the blade on and nip up finger tight and rotate by hand to check for wobble. If its too much slacken the nut, rotate the blade 1/8 of a turn relative to the shaft and try again. Keep going till you hit a "sweet spot". You may need to do similar with the drive washer. By this means I got total side-to-side wobble down to 1/10 mm - which is as close to zero as you could wish. Its all too random and a lot of hassle, but the blade did remain undisturbed for the whole job. A better shaft design is needed, no doubt more expensive, and I guess a lot of these cheaper machines will be similar in construction so I wasn't keen to look around further.
One other thing with this machine is its plastic chassis, to which the table and motor are independently bolted. There being no rigid machined cast metal connection between the two, it was not surprising to note that the plane of the blade was not perfectly aligned with the machined grooves in the table, so you need to allow for this when setting the fence.