What is the purpose of LiveCDs?
Live CD's can be a good indicator of default hardware detection but not only is there no guarantee that the full install will work for sure, there are sometimes other options that may or may not work for you on an installed system. When I was a new Linux user I found default compatibility desirable and I still do.
Using a live CD as a hardware detection indicator is far from their only function. I was very glad to have a Knoppix CD when 2 hard drives died within a week.
Your real question of why a Linux CD cannot offer you the end-all of hardware functionallity, while not completely unreasonable, is just not realistic. There are free downloadable Linux versions (being also available as cheap CDs if you have bandwidth considerations) that would offer fuller options.
You have already won half the battle as you are well aware of the issue. The next step is to consider your options and make a decision which seems best. No matter if the decision is to investigate further or toss your live CDs into a drawer, as long as it is the best decision.
I would suggest either following up by trying the drivers you are aware of on a free download or perhaps seeing if an install to the live CD is possible to check it out.