For reference, I think the salt flats in Mad Max Fury Road was meant to be a dried up sea bed.
This will likely really happen. Yes, it is capable of creating the post apocalyptic environment you describe. And is, in my opinion, the most believable. This will shift plant-survivable habitats towards the poles, leaving what is currently tropical lands as desert.
Things about global warming that could kill plants:
- Plants die directly from heat/dehydration
- Plants die from fire caused by lack of water caused by heat
- Global warming causes change in winds that mean rain no longer visits certain areas
If you cut down all the trees, they aren't coming back, because there's no naturally occurring seed for them. Particularly with plants, removing large portions of their neighbours will hugely reduce their reproduction rates and, after a certain point, could remove all traces of particular species within a few generations.
It is possible that these two could combine to cause sudden and rapid disintegration of plants over a wide area. If we look at the IPCC reports, we can find a predicted temperature rise of about 3°C degrees by the end of the century. This may not sound like much, but the last ice age was only 4.5 degrees different to what it is now. So congratulations, your post apocalyptic world is fairly likely in the next hundred years.
For the purposes of dramatisation, I would suggest a period of little noticeable change, and then a sudden period where lots of things change. This is ideal for your story as there will be a sudden societal shift (eg governments fall, wars etc) when this change happens. Yes, this is one of the plausible things that happens, though I haven't found a good source on it.
Although not mentioned in any of the parts of the IPCC report read that I, a typical thing spouted by global warming activists is the snowball/runaway effect. In short: decreased size of polar ice caps means less reflective area means higher temperature means decreased size of polar ice caps. Or: reduced number of trees has reduced number of seedlings has reduced number of trees for the next generation. This makes good story material.
There are supportive feedback loops as well though, trees are known to produce more oxygen in higher CO2 environments, so it isn't all doom and gloom. I trust the guys at IPCC to know what they're talking about, so if you want actual facts go read their extremely comprehensive reports.
A specialised bacteria wipes out everything with cell walls (aka all plants).
Move the Earth closer to the sun:
Nukes, asteroid impact, villainous plans involving really big rockets....
Radioactive Fallout that decays rapidly: Humans live in bunkers for a few years, so they survive, but not much outside does.