This is true for the Sport fisherman but not the commercial Long-line fisherman.  The Circle hook was developed for unmanned fishing lines that had to wait for long periods of time before being harvested.  During this time, the conventional style hooks could work loose and fall out.  Also, fish that are deep hooked will waist a lot of time for commercial fishermen and is often the case when unattended. In other words, it was not adopted for its quick hooking properties but more for unattended lines and its holding   properties.
For the Sport fisherman, it is to protect the fish from unnecessary damage due to deep hooking and for a live release.  I support this, but if you want to put more fish in the box, you had better stick with a conventual hook.  In areas where you can let the fish chew, a circle hook can work well but this is seldom the case when structure fishing in Florida.  Fish like grouper need to be struck instantly to keep them from moving you under the structure. Using a circle hook will mean more missed fish; this is the price you should expect to pay when using them. It is a matter of physics!   The circle hook point is bent over and has a blind spot.  It is best set by letting the fish swim away so the hook point misses everything but the jaw bone.

Deep-water fish should not be fished just for fun because bringing them to the surface puts them in more peril than where you hooked them.

Barbless hooks are a good alternative to circle hooks.  Barbless hooks make it easy to release a fish at the boat without handling or ripping a large hole in its mouth.  If your fish is hooked deep, cut the leader close to the hook and let the fish go.  Saltwater fish can usually dissolve or pass a (non-stainless steel) barbless hook.  It is a fact that a skilled fisherman can put more fish in the box with a barbless hook than a barbed hook.  This is due to being able to set the hook easier and unhook the fish faster.  You just need to know how to keep a tight line from set to box.  With a barbless hook you can have the best of both worlds.

Deep hooking a fish is unwanted regardless of what you intend to do with the fish.  You can avoid a lot of it by paying more attention to what is going on down below and setting your hook sooner.  You cannot be a hundred percent but I find that most anglers are asleep at the switch or waiting for the fish to set the hook, thus a deep hooked fish.  Some of the key words here would be "awareness" and "focus".