I am finding it hard to comprehend people's obsession and reasoning behind having a strong tail even at expense of leaving out better bowlers...

(if the the top and middle order struggles against spin, then in all likelihood so will the tail)
I keep hearing people (experts too) say that playing both Finn (if fit) and Monty in the next game would gravely weaken their batting unit. Do they, however, realize how much of a difference this move could make to their bowling. For example, although they'd likely lose 30-40 runs playing the former two, they may manage to restrict India for 100+ fewer runs than with Broad and Bresnan instead. The positive impacts of the bowling performance may even carry into the batting. Hence, the potential gains from bowling clearly outweigh the additional runs that Broad and Bresnan would probably add to the tally. (It's not like they are in a good batting form either tbf)
If I were in charge, I'd play the 4 best bowlers for the conditions given, and not compromise bowling to strengthen the tail-end batting, especially considering that they are now 1-0 behind and they must take 20 wickets to win.
Play the best bowlers and play the best batsmen to give yourself the best shot at a competetitive performance, easy. Take out Patel too if he's not a better batting alternative to Morgan and co..