OP has found fault with every aspect of the flight. It is quite clear that CX is not up to his standards.
That is apparently doubly so because in his professional opinion, the diversion was not necessary because the "sick" passenger was sitting up on the gurney when offloaded.
The sole issue here is what happens when a misconnect (OP may want to correct the odd misspelling in his thread title !) caused by a delayed arrival. The answer is simply. It is CX's responsibility as the late delivering carrier. Has nothing to do with fault, simply an allocation of risk.
Bugging the crew was not necessary as there is nothing to be done. CX staff on the ground will handle rebooking and it is best to leave it at that.
Conversely, the whiners who don't like it that one can fly in CX on AS miles which one can purchase quite cheaply, should stop whining. That is a business decision taken by CX. AS and CX both know the situation, permit it and that is the end of it.