I only press what I can or won't order from board supplier. Such as fancy veneer layups where I want to control the veneer width for equal spacing, or when I want edges under my veneer. I will press laminate as well because I prefer PVA to contact.
Pros: veneer selection and layup control, option of edges first, arguably better material use.
Cons: time to piece, tape/stitch and press panels, a lot more sanding when using raw veneer. I cut bundles of veneer on my sliding saw and curly veneer can tear out necessitating a pass on the jointer and much grumbling from me. You need space for layup table, press, and place for sheets coming out of the press to equalize for a time. Removal of tape if you are using is slow, but then what were you going to do while you wait for the next load to come out.
I am not making a good case for pressing yourself am I? I used to work in a shop where we pressed everything. Dogmatic owner. He had a hot press with a seven minute cycle time, a Haug table top stitcher and me at $9/hr. I learned to veneer there and would not be without a press but I use it sparingly on projects that require the attention to detail and pay for the extra time required.
I hope this helps.
Tom