A transport is no different than amps or preamps with respect to the internal circuit components - the better the quality, the better the sound. This is because preserving an audio signal is is tricky (and expensive). A transport that sounds better does a better job of preserving the signal that it generates and transmits, meaning that the circuitry and power supply are designed to a higher level.
A transport will read the data off the disc and convert it to an electrical signal similar to that found in an amplifier, with some differences. The digital data stream read off a CD contains the "ones and zeros" which represent the music signal. But it also contains the critical timing data that tells the DAC exactly when to start the conversion process. If this clock signal is off, the DAC converts the signal too late or too early, resulting in distortion (jitter). Both the timing and music data are stored as one signal superimposed on one another. The transport, ideally, must recreate the waveform without any "overlaps". To do this, it has to have a very precise clocking circuitry.
There are many things that cause the timing signal not to coincide with the audio signal. One is the power supply. If it is not fast enough to switch at the right time or does not maintain a dead-on DC, the error results. The power supply is affected by the transport motor, the drawer motor, the panel LED circuits and other electrical devices (caps, inductors). Also, if the clock circuitry is not well designed, it will introduce errors in and of itself.
To minimize the errors, the circuiry requires a lot of thought and execution which means cost. Even if timing and music data are perfect, the signal still has to travel through the transport making it subject to distortion from circuit elements much in the same way as in other electronics. To preserve the signal path, again, expensive circuitry, highly regulated and discrete power supplies, and solid construction works best. Bottom line - design and parts quality affects all audio components.