I have said no such thing.So you're saying that a single battleship, damaged and leaking oil, would survive better in hostile waters than if it were escorted by a heavy cruiser ?
If you would take the time to re read what I have written you'll see that I am saying that PG could not protect Bismarck with her flak, but as an additional target would be a liability. Any ship under heavy air attack runs the risk of taking damage. Bismarck could take a fair pounding having been built to take it, but PG would not be so fortunate. Bismarck took five torpedo hits without coming near to sinking. PG would be lucky to survive if she took one under such circumstances. It would probably stop her and then the escorting aircraft would be faced with a choice, leave her to fend for herself and concentrate on the primary task of protecting the main asset or divide their defense and try to protect both. Alternatively they could leave Bismarck to fend for herself, she being much sturdier and concentrate their efforts on PG. Whichever way you look at it, PG would be a liability.
If Bismarck had headed north, it is unlikely that she would have escaped at all.
Let us examine the scene after Hood was sunk. If Lutjens had chosen to go back the way he came, Tovey would most certainly have been alerted and as he was somewhere to the south of Iceland with Victorious in company, he would have turned about ready to intercept at the eastern end of the Strait. Catalinas from Scotland would have been sent to cover both ends of the Strait in a continuous patrol, so that Bismarck would have been constantly shadowed from the moment she entered the Strait. Mine laying aircraft would be sent to stopper both ends, at the narrowest choke points formed by the mine fields and destroyers would be lying in wait outside. The ship could expect heavy attacks from Wellington bombers deployed from Scotland.
If Bismarck had turned east, to pass through the Iceland- Faroes/route she would have run slap into KGV and Victorious, plus a number of cruisers and destroyers. The same would apply if she tried the Faroe/Shetland route. With heavy and sustained air attacks and with scant chance of any intervention from the Luftwaffe on either route.
Bismarck's only advantage in the break out, lay in the fact that she held the initiative and Tovey could only follow and try to respond to her movements. If she turned back, Tovey would hold the initiative, because he would be ahead and be able to get everything into place fairly quickly, for an engagement, instructing his commanders to converge on a predictable point. In the open Atlantic such a task would be extremely complex.