When faced with an unachievable (in the real world) target and a draw's the best you can hope for, what's to stop batters just blocking any remotely dangerous ball into the ground and maybe having a swat at anything that looks safely playable?
Absolutely nothing, in theory. This is one of the few occasions where having a batsman like Boycott would have been quite useful (who, incidentally, I think I heard above the roar of the crowd when Cook gave his wicket away - apoplectic would be an understatement). The problem is, if you're a batsman like KP, or punchy bogan Warner, it's very hard to pull your own attacking game back, and often you'll see aggressive batsmen trying to be defensive, but looking tentative/nervous and just getting out, where if they'd tried their usual swashbuckling, they may well have scored heavily. This is why I continue to rate KP highly - defensive may not be his natural game, but he can do it, and do it well when needed. Compare that to other big hitters such as Warner and Watson and it's easy to see the difference.
I get what Cook was trying to do - trying to wrest the initiative away from Johnson. That's fine, but do it with the bad ball, and do it once you've played yourself in for long enough to be able to better judge the bounce. Cook's dismissal was one of the softest and most stupid I've ever had the displeasure of watching, especially given how the match was poised. Yes, he can hook and pull quite well, but there's a time and a place, and facing an ungettable total, or occupying the crease for two days to save the game, this was neither the time nor the place. A quick check of where the fielder was wouldn't have gone amiss either!
Perhaps after a few overs, when Johnson was a bit more tired, trying to hit him out of the attack would be a good idea. But I think Root and KP played it much better - defend against Johnson, and milk the guy at the other end. That's the way to play unplayable bowling: defend it, and get your runs off the other guy to relieve the pressure. I thought Johnson was going to lamp Smith after he gave KP those two sixes to let the batsmen off the hook.