I’m pretty sure we still have plants, though I admittedly haven’t been out of the house much.
A lot of carbon was also captured during the aptly-named Carboniferous Period 360-300 million years ago. Woody plants had just evolved, but microbes that could break them down had not. Thus, coal. An earlier drop in sea levels also caused carbonate (as in limestone, dolomite, and iron ores) to precipitate out. The combination of these effects pushed oxygen levels about 50% above present, allowing very large animals to evolve.
It's not totally impossible for coal to still form, but the conditions are far, far less favorable: microbes get everywhere and the woody plants have a lot less lignin now than they used to, which also makes them easier to decompose. So, yeah, we're pretty got what we got.
Interestingly, this has happened once before. There's a "coal gap" from about 250-230 million years ago during which little-to-no coal was formed in most places. I'm not sure if anyone is sure why; this is right at the time of the P-Tr extinction, so a lot was happening. One theory is that the ligninaceous plants went extinct or other conditions were much less conductive to coal formation.
(FYI: Not a paleontologist or anything like--just a scientist who liked dinos as a kid and remembered some keywords!)
A lot of carbon was also captured during the aptly-named Carboniferous Period 360-300 million years ago. Woody plants had just evolved, but microbes that could break them down had not. Thus, coal. An earlier drop in sea levels also caused carbonate (as in limestone, dolomite, and iron ores) to precipitate out. The combination of these effects pushed oxygen levels about 50% above present, allowing very large animals to evolve.