New
#1
Just guessing:
...it cost more to enclose that part
...it would be harder to swap the controller board
...the manufacturers win when you have to buy a new one
Heat dissipation is probably the main reason.
Just the card is exposed because there is no reason to cover it. As long as it installed properly nothing can short against it just like any other card or even the mobo In your PC.
This situation is hardly unique in computers. The motherboard and expansion cards are also fully exposed. About the only case where circuitry is enclosed is in the PSU and that is necessary for safety reasons. Outside of the PSU the highest voltage will be about 12 volts so safety is no concern. Completely enclosing the hard drive is unnecessary and would make cooling more difficult. As it is the HD platters and other sensitive components are protected.
I doubt hdd manufacturer's would consider putting a drive in a dock "proper" installation. The mfr designed the drive to be installed properly by properly trained people that know how to handle the drive. If someone that doesn't know the proper way to handle the drive handles or installs it incorrectly, it isn't the drive mfr's concern.
I've handled hundreds, if not thousands of cards and drives with exposed circuitry over my 30 year career and (to my knowledge) never had one fail because I handled it improperly.
There's no doubt that covering it up would protect it better but it isn't deemed necessary and would drive up the cost needlessly.