Hmm, if you have a 3" x 3" leg and then you cover each face with a 1" x 3" then you will not end up with a square leg, to do so you would require 1" x 4" 4 off or you'll need 2 off 1" x 3" and 2 off 1" x 5", so why not just with 5" x 5" legs and no face covering?
Err... complex design feature that i will try to explain.
And now we recurse right back to the "This is a BENCH. To WORK on. it is NOT fine cabinetry." part of the discussion. Tolerances of 1/4 INCH, not 1/4 mil are the norm here. Again, perspective, man. Lapping two planks together is a perfectly valid building technique, and it is how you MAKE straight lumber out of #2 pine. Once you build the shelves and cover them with gear, the wood they're hanging from will be the last thing you notice. It makes no difference if your posts wiggle 1/4" or even 1/2 an inch from one end to the other; what matters is how carefully you place the cleats for the shelves. This isn't rocket surgery; you're building a rock to lay the rocket ON while you operate.
If the posts are the LAST thing in your build, then you're building it WRONG. You'll never get it square & level if the posts are an afterthought. Instead of hating the look of the lumber, incorporate the look into your design. Post & beam is a classic architectural design; follow those principles and even if you are using the simplest building materials, it will come out looking stout and "heritage".
mnem
I am suddenly very, very tired.
OK so the complex design bit
4 legs held in place by a frame(white), then there is a cradle(purple) attached to the back of it for the posts and further strengthening of the frame, next comes the slats(gray) which are non-structural ie entirely for a small shelf, next the
top which is a layer of 1/2 in mdf 1 in white fir and 1.5 in pine, now come the
posts, with the top in place i can set them on the cradle and if that end is at least reasonably straight then getting it square will only be a matter of making sure it is sitting correctly and then double checking it to the top with a speed square. In the picture i used a 3x5 for pine and a 2x5 for hickory. In the case of pine i could add one more 1x3 onto the back that would screw directly onto the cradle and posts. Make any sense? Also i already have the cradle ready to go pretty much, bit late to change the plans.
As for why it has to be dead straight to the top? Probably just cause i'm obsessive compulsive.