I guess I was being a bit snarky earlier.
For some things, I can see waiting to package it up at the post office. Priority / Express Mail envelopes are a big one. Since I do a fair bit of shipping via USPS, I actually go down to the PO ahead of time and pick up boxes for the things I'm going to ship, and do all the packaging at home. That's how I'm acutely aware that they often don't have what I need at a particular location, which further reinforces my desire to pack things up at home.
I also don't trust the tape-strips that are pre-applied to the packaging. I've had some that stuck like glue, and some that started peeling open a minute after packing up my boxes. So, I always end up reinforcing with some shipping tape.
I grant you, I'm probably not the typical postal customer, though. The more casual user of postal services will probably scratch their heads over many of the things you've pointed out on the USPS site. I've been using it for so long, it all feels pretty natural to me.
I imagine the "no first class stamps at USPS.com" thingy is a concession to Pitney Bowes, Stamps.Com and other vendors they've made deals with for various first class postage services. Otherwise, there'd be little reason for those other services to exist.