Using premix, the amount of lubrication is determined by the throttle alone; using the pump, the lubrication is determined by the throttle setting AND the rpm.
The oil pump insures that there's adequate lubrication for the bottom end and pistons when the motor is at high revs with the throttle closed, like slowing from a high speed on the highway to make a slow turnoff or stop for a traffic signal. Downshifting a 2-stroke for engine braking is useless- there isn't any- and hard on the motor- the revs go high with the throttle closed; oil pumps help keep the motor unstuck when someone who hasn't learned how to live with a 2-stroke is at the controls and does that. Downshifting keeps the transmission in the right gear for the bike's diminishing speed, but letting the clutch out ought to be done only when accelerating again from a slow speed after having selected the correct lower gears as the road speed diminished so as to be ready when the situation warranted getting back on the gas again.
Modern 2-stroke lube is such a good lubricant that some of this problem is alleviated, but the motor can still be starved for oil when you close the throttle at high speed using pre-mix. Richer idle jets or idle needle valve setting and enlightened throttle management can prevent seizing, but it's even more sensible to keep a finger or 2 on the clutch lever at all times when riding a 2-stroke that originally had an oil pump but it was removed. Actually that's a good idea anytime, on a 2-stroke, especially one that's been modified in some way to run hotter- freer air cleaners, for example, or using an aftermarket tuned exhaust system.
The mass of air cooled two-stroke cylinders is unavoidably asymmetrically distributed due to the bypass ports, so they change shape a little when they expand with the heat of running. The bore must be a circle in cross section when it's hot, so it has to be machined a little oversized when it's cold and thus not precisely round, which is why big-bore 2-strokes rattle and clang a lot when they're first started- the piston is round, the bore is not but it's large enough so the piston can move freely, loose enough to "slap" until the cylinder is up to operating temperature and so the bore is therefore closer to being round. In the past, piston-to-bore clearances were larger in 2-strokes than they were for 4-strokes to help prevent oil starved seizing; oil pumps helped make that somewhat unnecessary which lessened the chance of seizing and made the motors mechanically quieter and less annoying. Such altered motors are more susceptible to oiling problems than those designed out front to run premix because their piston-to-bore clearances are a little tighter. Of course, liquid-cooled motors avoid a lot of these issues since the range of their operating temperature is much narrower.
You can get away with taking the pump off and using premix, but there are a lot of factors involved. I'd keep the pump. In fact I've kept the pump on all the 2-strokes I own except one- that's 4 out of 5.