I had one board which differed too much in dimension, decided to replace it and my glue-up is ready. Decided to leave everything in the rough biggest difference is around 1/32" so we will play with hand planes, the exercise will do me good.
That's one way of looking at it.
I have never used cauls, good idea one day.
Cauls will save your butt. Using them is about as accurate of a way possible to get good alignment. I wouldn't do even a simple glue up without setting up for their use. Besides just using a straight edge, very thin shims make the process more precise, and less of a chance for mis-alignment.
I use a joint bit in my shaper, which is very forgiving, it aligns both the boards and prevents cupping, even if you clamp wrong. The joint kind of fixes that.
I've used that type of bit in both a shaper and a router table and it's not forgiving at all. You wind up with what you machined, and there is no fudge factor.
Joint bits are used a lot in Europe, but not well known in the US. If you don't know their tricks, you will probably end up throwing them in the trash and never try again.
You might have just found out about joint bits. They may be used in Europe, but they have been used here in the US for as long as I can remember. It's not like a revelation that the idea has just crept up on our shores, making their use a whole new experience.
In using that bit, the recommended steps would be to plane for thickness first. Reason being, that the alignment of the parts after machining depends on the bit being centered to the edge of the board. Used in a table, the board gets machined one side, and the mating board gets flipped to the other side. The possibility of misalignment of the machined edge is prevalent with any deflection in the length of the run, or operator error. There's very little that can be done once the joint(s) have been machined.
In a perfect world, with perfect stock, and a perfect operator, I still wouldn't use that bit for gluing up panels. All can be going so well, and...oops...there goes the edge with a little tear out. The process can turn out to be one big fire drill, costing time and materials.