Probably some confusion about terms in this thread, as well as how ignition systems work in general.
Points:
Contact
point switch 12v power to the coils to store energy, and when the contacts open, the energy stored in the coils, creates spark.
Transistor ignition:
The switching function of points can be replaced with an electronic or transistor type switch. These switch the same 12v power to coils, which operates in very much the same way as they did with points. The coil drive transistor can then be operated by a hall effect device, reluctor, or optical switch to control the transistor in time with the crankshaft position.
CDI is a specific type.
Capacitor Discharge Ignition It generally uses a circuit to step up the 12 v fed it, to store a 250-400V charge in a capacitor. The energy in this system is not stored in the coil to create spark. Instead the coil simply
steps up the voltage it is fed as a simple multiplier device. (Technically, this is more aptly termed a pulse transformer, whereas the points and transistor coils are more properly termed storage inductors.
Coil details:
The traditional storage inductor coil amplifies the 12V to a spark inducing voltage, by means of a turns ratio. In simplified terms, if there were 100 turns, wraps, or coils of wire on the primary and 100,000 turns on the secondary, this would be a ratio of 1000 to 1. Such a coil/transformer would convert 12V to 12,000V during operation.
For discussion sake, let's say that the goal was to produce 12,000V at the spark gaps. A CDI driving a pulse coil with 300V, would only require a coil turns ratio of 40:1.
Using such a CDI pulse coil with a 12V drive type (points or transistor) would only produce 480V, which is very unlikely to produce spark across a .050" gap.
Oddly, using a storage inductor coil (rather than the pulse transformer) is possible with CDI drive unit. Although the coil construction specifics do interfere with ideal operation, stepping up the 300V at the turns ratio used by the 12v drive system, does produce a rather impressive spark voltage at the spark plugs.
I have many coils from newer bikes on my CB750s without a problem!
Much depends on what is or is not encompassed by "problem".
Many of the transistor type systems use coils of lower primary resistance than do points systems. The lower resistance trades coil primary current, for a higher turns ratio, leading to a higher spark voltage potential. (This voltage "potential" is not guaranteed by the coil, however. It is only available if demanded by the ignition system; more later.)
The transistors used are chosen to survive the current demanded by the coil specified for the system. A points contact set switching higher current will heat more and deform its contacts at a faster rate than with the lower ohm coils they were designed to power and control. The lower the coil primary resistance, the faster the points will deteriorate. This is not a "problem" for those seeing the engine run initially. But, IS a problem for those wishing to operate points without replacement for the longest possible time.
Voltage potential:
For point and transistor systems, the spark energy is stored in the coil until the coil is "fired". The "firing" is actually the collapse of the electromagnetic field that the coil has stored. The coil output voltage rises as the field collapses until the voltage is sufficient to jump the gap at both spark plugs (SOHC4). This is when current begins to flow, and the current drain prevents further voltage increases. So, it is said that in this system, the GAP determines the voltage developed in the ignition system. Therefore, a coil that is capable of producing 50000 volts, with only produce whatever the gap demands. If that is 9000 Volts, that is all a "50,000" volt coil will produce in actual operation. However, because the GAP determines voltage developed, making the spark gap larger, raises the voltage development. A 50,000 volt coil will only make that rated voltage if the spark gaps are widened (or combustion conditions altered) to require it.