On the contrary Bazball needs a world class keeper more than a batter who can keep adequately. It’s no use piling on runs at a quick rate if you can’t apply pressure with the ball and in the field. Their ability to squeeze teams out under scorecard and rate pressure (a very novel concept in test cricket I must say) and pick up wickets with the ball has been a defining feature of the regime. Foakes was also a more sedate batter by Bazball standards who offered a good counterbalance to the others trying to go ham, it didn’t matter that Stokes would get out trying something crazy in his 20s or 30s as long as that allowed Foakes to build a base at the other end and equally Foakes’ presence meant that Bazball had a form of security in the lower order. Watling was the preferred keeper in Baz’s test side for a reason despite him being the antithesis of his approach in the past.
I assume they’ve observed Bairstow keenly enough in training that he’s impressed them with the gloves to get them enough dismissals that matter whilst offering a significant upside with the bat that other teams can only dream of. I also hope for their sake that Stokes returns to batting in more conventional fashion with Bairstow taking on the crazy role instead especially if the former isn’t going to bowl much. He could offer what Foakes did with the bat easily enough if he puts his mind to it.
Crawley’s seeing off 35 deliveries on average since Bazball began and has scored around 25 runs per innings for them. Your assumptions on his output are mildly exaggerated to say the least. Comparing him to Duckett, the latter sees off 59 deliveries and scores around 58 runs per innings for them. Heck, the other opener they dropped for being useless in Alex Lees saw off ten deliveries more compared to Crawley for the same run output. The much maligned KL Rahul whose highest score is 23 in this time period and could barely score also sees off five more deliveries compared to Crawley.
Let us go even further and compare more. Looking at test openers who did equally bad or worse since Bazball began… Rahul, Joy, Erwee, Young and Lees have all been dropped, a couple of them probably having lost their test careers forever. Tamim and Warner are around because of their past legacy and the latter has already been subjected to loud calls to be dropped. Shanto and Masood have been moved to other positions, Elgar lost his captaincy in a very public manner and is only around because the team direly needs all the experience until he is phased out. The Zimbabwean and Irish openers remain because everyone else is worse in their setup which leaves us with Oshada Fernando whose continued selection is the weirdest consistent thing SLC keeps doing for some reason whilst they experiment with ten other weird ideas elsewhere.
Quite simply put, there is no rational or tactical explanation for Crawley being an England test opener in this day and age under any kind of special role. The only reason he remains is either because the ECB and everyone else is too invested in him at this point and are suffering from sunk cost fallacy effects or because he is the world’s greatest nets batter who hasn’t cracked the code to replicating that on an open field with crowds yet. Or it could just be because of his dad and Rob Key, stranger things have happened.