It's not a matter of whether we can take great photos in JPG - of course we can, and people do, every day. I also have a friend who does brilliant work with a pinhole camera. Trying to do great work when your equipment has limitations is almost undoubtedly going to raise your art, whether you're a student or master.
My problem with JPG (and MPEG) is, and always shall be, data destruction. Terms like "lossy compression" don't go far enough - that's still too much marketing spin for my taste. Bits go out, and they don't come back. Intentionally. One of the fundamental benefits of digital over analog is there is no generation-to-generation degradation (well, bits can still get lost and, hopefully, error-corrected, but it's no longer inherent in the process). Lossy compression is an unwelcome reminder of the bad old days.
As the OP's example images clearly show, if you don't have fine gradation in the initial JPG, it only gets worse when you try to fix it in post. And fine gradation is the first thing to go. It's built into the JPG (and MPEG) algorithms.
Now, some of the best shots I've taken were shot JPG with a small-sensor super-zoom. It's the camera I had. It was hard to justify the expense of a full-frame Nikon when my output was destined for 150kb 72 dpi files for the web, and 1" x 1.5" "prints" via a 150-line half-tone screen onto matte book stock. CF cards were far more expensive back then (anyone remember the 1GB CF micro drive?)... Lots of rationalizations. But I also know how much better the results could have been, if only I'd looked beyond immediate end-usage, or my current skill with image editing software. I'd like to make exhibition-sized prints of those great shots, but they'd look like utter crap.
The principal reasons JPG and MPEG exist were the costs of data storage and data transmission bandwidth, and processor speed, back in the day. It's an exercise in, "Considering the costs, 'good enough' will have to do."
Well, we can afford better today. We can afford to shoot RAW + JPG, we're gearing-up for 4K video streaming... "JPG is good enough" just doesn't cut it anymore.