Whilst I am never going to suggest that I have superior experience or knowledge to the Pardeys, a few questions/comments on my own limited experience.
In some instances they didn't put put a sea anchor or drogue, even it horrendous winds. When they did put out a drogue it turned out to be much more difficult to retrieve than the sea anchor.
First question is when does "heaving to" become "lying to a sea anchor"? Seems to me the distinction has been lost in some of the examples given.
The main point that made more sense than anything else is that it is very foolish to try and outrun a storm. In almost every instance, boats trying to outrun ocean storms were severely damaged, many crew members were injured, some were killed and there were a fair number of boats sunk.
When does "running with" turn into "trying to outrun" a storm? I have only been caught in one bad storm (70 gusting 80 with 30 - 40ft, occasionally breaking seas). We sailed at 9kn under bare poles and the boat was threatening to surf, pitch dark, I decided to heave to. We got slammed by a huge broken wave (white water) and then by a wave that actually broke against the side of the boat with enough force to knock cabinetry off the walls.
When you are trying to outrun a storm you are going in the same direction as the storm itself, thus exposing yourself and crew to longer periods of nasty conditions.
So I decided to run at an angle to the weather and to slow the boat down with drogues to about 3 - 4kn. Using the age-old Ballot & Buys rule, we estimated the position of the storm centre then sailed away from it. It was that successful that this is now my stated policy on heavy weather management (with due respect to the Pardeys). I don't own a sea anchor.
Another thing that bothers me is when I watch systems moving across the Pacific to the immediate north of us, they sometimes take several days to move relatively small distances. In the infamous Queens Birthday storm north of New Zealand some years ago, boats were hove to and stayed in horrendous weather (80kn +) for three or four days while the system "parked" over them. Some of those boats were lost.
So like all things, heaving to is not the silver bullet that keeps one safe when things get really tough (IMHO).