Why do modern computer cases still have USB 2.0 ports?

Nobody has mentioned this yet, but USB 3.0 ports can cause issues with certain installation media (cough Windows 7 cough) where only USB 2.0 drivers are provided on the installation media.

Another key point mentioned by @togh is that USB 3.0 requires a large amount of bandwidth, which can congest existing PCI-E lanes if all of the USB 3.0 ports are in use. Using 2.0 (with it's lower bandwidth) allows more devices to be used (which may not necessarily need the high bandwidth USB 3.0 provides; e.g. most user input devices) while maintaining open PCI-E lanes for other peripherals.

USB 3.0 does have backwards compatibility, but if you, for some reason, happen to buy a motherboard that does not have a USB 3.0 header connection (only back I/O USB 3.0 ports), you're left without any front panel USB ports at all. That's one possible explanation.

No, there is no reason - except cost.

There is no technical advantage from having a USB 2.0 port instead of a USB 3.0 port; but it is also not a big selling point to upgrade all ports instead of some only, so the extra effort of redesigning the hardware layout to have only USB 3.0 ports is often delayed or avoided.

As others pointed out, most people assign devices to the ports that would have no advantage of USB 3.0, so they don't care about the ‘limitation.’

If I'm designing a computer, I would not design any USB 2.0 in there; actually, there are many computers that do not have USB 2.0 anymore (mine doesn't). It just depends which ones you check.

My impression is that the market for towers is generally receding, and losing to laptops; little is done to their design therefore. Laptops are not more expensive anymore and much more practical.