Thanks for drawing my attention to this.
I went back and listened to some Sinatra and found All or Nothing at All (from Sinatra and Strings, 1961/1962, be careful he recorded it many times).
There is a buildup of strings at the beginning and then they stop, revealing the deep reverb from the session. Worth listening to just to hear the reverb.
My feeling is they (the whole production team) really learned how to work with what they had. The arrangement, the musicians, the room, the equipment, etc. The equipment was simple but the usage was maximized.