How can an active preamp possibly help?

Exactly, a poor impedance matching will cause distortion. Remember: impedance is a function of frequency, therefore a good matching across the audo spectrum is important. Be sure you know what you are doing when go passive. One or two resistors do not necessarily mean "shorter path" than a few active transistors. If poor matched, it can be a "distorted path".

It is like to drive a low efficiency speakers with set amp, a wrong combo still makes bad sound.

If the output of a CD player ( or any other line level device ) can EASILY drive an amp to clipping and beyond with normal signal levels, it should be fine to use in "direct drive" mode. As Twl points out though, you may have to pay attention to line lengths and impedances to obtain optimum results.

Other than that, some analogue outputs on CD players, etc... with built in potentiometers are of low quality. Obviously, if you spend the money on a more expensive unit, "chances are" that they will have used ( hopefully ) good quality components.

Just keep in mind that some CD players do NOT output as much voltage as they are rated for. On the same hand, some power amps require more voltage to attain full power than other amps. Mating a "weak" CD player with an insensitive power amp will typically result in the loss of dynamics / flat sound that many here have commented on. One can somewhat "make" this type of situation occur due to impedance mismatches between the CD output and amplifier input. In order to get around this, a CD player or DAC should be able to deliver at least 3 - 4 volts of output without putting up a fuss. If you can do this, you should have plenty of gain to compensate for even those "quietly recorded" CD's and slight impedance mismatches. In such a situation, you will still probably even be able to overcome major impedance mismatches but sonics ( tonal balance and transient response ) may suffer. Sean
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I like to simplify the ACTIVE VS PASSIVE (or dirrect source to amp) scenario like this:
...with out being technical, it's usually like the difference between a HONDA Civic that can over rev it's engine and RPMs while going 120mph, vs a Turbo Porche that has much more snap,torque, overall power, response, and performance at the same 120mph!!!
In the case of most passive set ups(or no-preamp set ups), sure you can get the overall volume level up. But what seems to happen is a lack of overall dynamic control and body to the sound, which an Active preamp set up can overcome by proper amplification of it's signal! Even weaker amplifiers with higher wattage ratings can push the volume level higher, but it's also flat and 2 dimmenstional, and strained as well! (i.e, cheap reveiver amps). I'm also not so sure that just having PROPER IMPEDANCE MATCHING is the key. I think you can still get a good impedence matcy between CD player and amp, and still not get the dynamics you would from a properly designed active preamp! Hum....
Also, for the record, I've talked to PLENTY of aduio engineers and speaker/equipment designers over the years, and they often think things are a matter of simple mathematical and physics equasions! What I find is that usally these are the guys that don't have the best sound from their systems also! There's an old saying.."if it ain't broke, don't fix it!" And the quality active preamp works for all practical purposes!
Anyway, I've yet to hear even the expensive Wadia's sound as good dirrect to an amp, as they do with a good preamp infront of it! That's what I find anyway. And I've heard a lot of passive set ups!...a lot!
THE ONLY way you'll find out the differnce, is to try both, experiment, and then you'll know!
good luck