It all depends on the tires you're running. Sorta brief explanation:
Every tire has a load rating at a certain psi. For a made up example, a goodyear eagle in size 205/50/15 can hold a maximum of 1200 lbs at 44 psi. This does not mean you need to inflate that tire to 44 psi on a CRX. Reason is because a CRX only puts down about 600lbs per front tire and 400lbs per rear tire. If you inflate the tire to 44psi, there's a chance the contact patch will no longer sit flat and true on the pavement and will begin to balloon outward. This will lead to premature wear in the center run of the tire.
44 psi causing abnormal wear might be exaggerated but it illustrates what overinflation can do to tire wear. I'm sure the governing agencies that oversee tire construction and performance require that a tire must sit flat throughout a range of psi's regardless the weight being put on it so long as it's within that tires load rating.
That being said, I think a lighter car doesn't require as much psi to achieve proper inflation and performance levels so I wouldn't put in 40+ psi. It's difficult to judge what psi you get the best compromise of rigidity/performance/life for a certain tire for a certain car of a certain weight short of engineers and track times. It's always a safe bet to go with recommended pressures because no matter what tire you put in the wheel well, you're within Honda's tolerance range.
ummm... I take the "sorta brief" back.