Edgar T Westbury wrote this:

Crankcase compression
The limitation in volumetric effeciency of two-stroke engines is primarily due to the incomplete charging of the cylinder by using the crankcase as a pump. Apart from the loss of effective volume through imperfect port timing, the necessary clearance space to accommodate working parts imposes a limit on the pressure which can be produced in the crankcase. Many designers have taken staps, sometimes drastic, to reduce crankcase clearance to the bare minimum in order to improve both suction and pressure effects.
While these measures are often beneficial, they may in some cases defeat their own purpose by increasing the load involved in charging. The function of the crankcase is not so much that of a pressure pump as a displacer, and work done in producing pressure is a dead loss from the aspect of mechanical efficiency, which is one of the virtues of the simple two-stroke. Unfortunately, a certain amount of pressure is necessary to charge the cylinder in the very brief period allowed for transfer port timing, in a high speed engine; but, again, too high a transfer pressure may cause turbulence in the port and impair scavenging.

Attempts have often been made to improve the volumetric efficiency of two-stoke engines by using an oversize charging pump of some kind. This may take the form of a separate charging cylinder, as in the original engine by Dugold Clerk, or a rotary blower. Alternatively, crankcase displacement can be increased by adding a crank or or eccentric driven displacer piston, or using a stepped main piston. This was done in the Dunelt motor-cycle, which had a certain vogue in the 1920's, but did not prove the advantages of the method. Such engines have sometimes beeen described as "supercharged" but this term is more correctly applied to engines in which the cylinder is charged at more than atmospheric pressure.

This is clearly impossible in normal two-strokes in which exhaust and ports are open simultaneously. They can, however, be "super-scavenged" by an oversize charging pump, often with some advantage, but at the expense of economy, because wastage of fuel through the exhaust port is inevitably increased. This may be tolerated in racing engines, and is no disadvantage in diesel engines of the injection type, which are charged with air only. In my experiments, however, I have failed to obtain any substantial increase of performance in two-strokes by increasing the charging pump volume.

It is a waste of money to buy the "supercharger" and it is a business for the maker who are producing the "supercharger" who are not giving the effect of the two stroke engine cause all ports are still open.

Edit: missed some text..