I've had many CD players with variable volume control connected directly to power amps. If you have a single source system (CD only) it can be a very economical way to go. You obviously save the cost of an extra interconnect cable and pre-amp. I've always enjoyed the added transparency that this type of setup has provided. However, added transparency may not be a good thing if you listen to a lot of CDs that are not well recorded.
The downside typically mentioned is that many people feel that a quality pre-amp adds an additional level of dynamics to the sound. This may or may not be needed depending on the type of music you typically enjoy on your system. I would think it would be most important with classical, but I don't listen to much classical, so I've never wanted for added dynamics.
A good friend of mine has a very highly resolving system using CD-direct to amp. He recently built a simple tube buffer to place between his DAC and amplifier and he swears that it is one of the biggest improvements he's ever noticed in his system. So, if you try CD-direct and the music seems to need more drive or dynamics, maybe a tube buffer would suffice. I've never used one, but I often see the Musical Fidelity tube buffers for sale here on the 'goN.
Enjoy,
TIC