I also like the strings on All I Ask, and for that matter also on You're the One to Make Me Cry. I appreciate them from an arranger's craft standpoint...it's continuing the tradition of Nelson Riddle's string arrangements with the old crooners like Sinatra. In fact, I forget who it is but the guy who arranged the strings for All I Ask, who was very old at the time, was a very famous arranger and had worked on lots of classic old records.
I also don't quite get the "sappy" label because there's a fair amount of jazz-like dissonance in that arrangement, which keeps it way more interesting than it might have been.