Is there a reason not to use the hibernation in Windows?

Generally there is no reason not to use it. Just keep in mind, that there are cases, that it won't work as expected.

These apply both for hibernation and suspend (to RAM):

• some applications are not hibernation-aware. Eg. games tend to crash.
• some WiFi drivers have trouble with hibernation.
• networked applications loose connection and most do not reconnect automatically.
• DHCP is not invoked, old IP is used, which by then might have been reassigned.

Hibernation vs suspend:

• wake up from suspend is immediate, hibernation must load from HDD.
• for hibernation you need space on HDD (a least of a size of memory occupied).
• hibernation consumes no power at all, while suspend consumes minimal power (few Watts).

If your computer is capable of S3 Sleep (ultra-low power consumption) there isn't a compelling reason for a desktop to be placed in hibernation. Hibernation has a high user impact, as it generally takes 1+ minute to wake up.

If you're using a laptop, and you need to use full-disk encryption to protect customer or other data, you absolutely must enable hibernation and disable sleep. Why? A sleeping laptop can be woken up to a boot prompt/screen lock screen, at which point an attacker can capture the drive's encryption key via Firewire port or by exploiting a Windows, application or other OS vulnerability.

This may seem far-fetched, but tools are easily downloadable to do these things, and any attacker targeting you is capable of this.