The article mentions "EPTT" (AT&T's own acronym for what it likes to call "enhanced" PTT). The "enhanced" part really refers to additional business-class features recently added by AT&T, things like interoperability with LMR (land mobile radio), integration with workforce field tracking & time reporting, etc.—capabilities that Nextel had ten or more years ago.
I tried AT&T's "EPTT" in a local AT&T store, coincidentally in an area with no LTE service yet, so it was operating on the 3G AT&T network. The performance could only be described as "push-to-wait...and then some". Initial PTT "setup times" on four different phones they demonstrated for me were on the order of ten seconds to establish first connection. When you're accustomed to N... (continues)
The PTT app itself was a little slow to open, but I didn't have any of the problems you mention with call setup times. I'd say they averaged 1 - 2 seconds at most. It's not lightning quick, bu it seemed acceptable to me.