Doable, and might even be a good idea for long thin PCBs, but it messes with both your routing and placement and therefore consumes PCB area. Also upsets your controlled-impedance traces. And adds an extra assembly step. To estimate doing this, take the PCB image and Paint and try to clear a 3mm gap in it. How many components do you have to move? Do you have to make the whole thing 3mm longer? Aren't most of them decoupling capacitors that must be kept right next to their corresponding IC?

(Look at the smallest .04 x .02 resistors on there!)

More cynically, the PCB only needs to be made as bend-resistant as the display: you don't care about your BGAs if you've cracked the screen.

The article does mention a fix the repairers have been applying, involving the "sticker shield" - not shown in the hero image, it's the metal casing that's been removed and you can see the edges of. That's a few mils off the surface of the PCB and evidently stiffens it enough (on the I-beam principle of operation) to avert the problem.