I do 1/2" Baltic birch for drawers 98% of the time. As far as S4S is concerned, my local suppliers are very consistent with thickness, much more so than S2S and S2sR1.
And yes, the planer is very useful for those odd sizes and or from rough cut to S2S.
I do a lot of resawing of 4/4 I can get a nice thick veneer and 1/2" material from that.
At Christmas I usually build boxes to give to friends and family. These, below were from scraps. The 2 strained boxes with veneered tops and bottoms were from S4S poplar 3/4" thick. A piece of 1x8 12" long build a box.