Planets which have something that we might consider to all be a single climate given the way we classify things based on earth is entirely plausible, for certain climates at least.
Mars easily qualifies as a desert over its entire surface. There is climate variation, but all of it is something we would call "desert".
Similarly, you could have more water to the point it covers everything and the entire planet would be ocean (which isn't exactly a climate in and of itself). But oceans can have varying climates. Variations based on depth, insolation, currents, etc. The intertropical convergence zone would likely be a massive band band of thunderstorms. Then you'd have calm doldrums, and then utterly mid latitudes where massive hurricanes sweep across periodically.
A global swamp or jungle though doesn't seem workable. A global wetland would need an almost perfectly smooth planet where everything was in an absolutely perfect balance. "Jungle" is fairly specific and tied to the specific nature of life on the planet. Both global jungle and global wetland have the severe problem of where you maintain a reservoir of water to generate the rain with oceans.
Making a single climate planet habitable is also problematic. Without phytoplankton and forests, a desert planet isn't going to have an oxygen rich atmosphere, unless you do something strange like the Sand Worms of Arrakis in Dune which produce ridiculous amounts of oxygen. Then again they are generally just ridiculous creatures so you might as well just declare that where the oxygen comes from is irrelevant to the story. One might say that Arrakis isn't functionally a desert for its native life because lack of water is irrelevant to them.
What makes a place a "functional desert" is extreme scarcity of a resource life needs, but which can be gathered, retained, and re-used. Most likely a solvent or other medium within which biological chemistry occurs. It's improbably that life would originate on a planet which is entirely functionally desert for that life.