I can't make an overly stiff frame soft enough with a change of strings to make me like the frame. The same goes for a flexible frame that cannot be changed enough by string tension or type to stop that trampoline effect. Maybe a frame that has all of the mid range attributes of moderate head light balance, and flex combined with weight to allow you to choose it's best characteristic with the right string and tension is the ideal and could be seen as string sensitive. Or taken the other way, a stiff and powerful frame can be ruined with rotgut string at the wrong tension just as a sponge bucket frame can be made to lose all feel with the wrong tension and poly.
The best answer is to experiment and test different frames that augment and compliment your game taking into account any predisposition toward injuries you may have. You can always change the characteristics of weight and balance but changing racket flexibility doesn't happen. You can loosen strings to reduce shock but at some point it will alter your stroke results and may require a change of approach which at that point might be best to consider a change of rackets.