But you might not increase it enough, and you might not increase it usefully. Airflow through many cases is impeded by tons of cables. Even if all you've got is a hard drive and a CD-ROM running from the one IDE ribbon cable, that plus the floppy drive ribbon cable and the various used and unused power supply cables can significantly slow air flow. And, even if you route and bundle your cables carefully, airflow oddities may mean that a lot of the air passes over nothing that needs it. Generally speaking, electronic equipment works less well the warmer it gets.
More heat means more resistance.
Electrons have a harder and harder time moving through a conductor the warmer it gets. In the case of PCs, though, it's not a simple proportional situation, and different components care about heat to different amounts. Hard drive motors and bearings are made to tolerate considerable thermal expansion. CPUs have core shutdown temperatures hotter than most people's hot water. Even things like CD writers, which originally needed to be mounted in separately cooled external cases for reliable operation, now put up with sharing the silicon sauna with everything else.