If you look at your work in the context of time, it may help you decide. There is also a historical context.
If your work is expected to last lifetimes, then more robust standards apply that would certainly exclude peel and stick or contact. If your work is short-lived - destined to be removed in a few years, or end up on the curb, then perhaps peel and stick/contact is a viable method. Of course, this assumes you are okay with disposable resources - your time and the wood products.
Historically, veneer slicers outpaced glues in the early 20th century and made for a lot of furniture that was 'papered' over with veneer to dress it up. The poor quality glues caused the veneers to catch and peel, and gave veneer a bad name. It wasn't until after WW2 that glues became better and techniques advanced to make a better veneered product. However, the notion of 'cheap veneer' is still out there.
I think you will find that better craftsmen (better in the eyes of their peers) and professionals will use presses and more industrial methods of veneer application, and those that are new, naive or unaware are more likely to use peel and stick or contact cement.