How was it implied unless you've read technical manuals? During TNG they max out at warp 9-point-something, passing warp 10 once in "Where No One Has Gone Before". In AGT they go to warp 13 which isn't treated like a big deal at all - it's just four warp factors faster than they could go 25 years earlier.
Agreed that it was Voyager that made a Trekking across the galaxy a lifelong journey. That's the only time those warp scales have been taken seriously. DS9 made the "long way" trip to the other end of the wormhole a lifelong journey too, but they merrily hopped from DS9 to Bajor, Earth, Romulus, Kronos, Cardassia and others all in the space of a scene break, and often by Runabout!
Missed this one:
"Thrusters on full."
Although a little weird, I figure it's a STIV reference - "He's not exactly working on all thrusters!"
This new young crew very much is.