Stun, Daze and similar stuff don't impede your movement...
...they make your mind funny.
While you are stunned, there's nothing holding your body to move. You just can't think right to actually do something. If you take a really hard blow to your head, that won't make your body harder to move - it will make your brain go gonzo for a few secs, before you became aware of what's really happening.
Stun is not about movement, is about senses of what's going on.
Freedom of Movement makes "your body work right", not anything else. It allows you to move, but not allows you to think. You can't think if you're dead. Or Stunned.
Paralysis don't block purely mental actions, so it don't block "thinking".
Slow makes your body... well, slower, but it doesn't affect your thinking.
Web is... well, a web. It hinders your body, not your mind.
Stun, Daze, Dazzle and similar stuff, on the other hand, makes your senses go wacko, so they aren't really blocking your movement. Stun never stopped you from moving, it just stopped you from thinking for a while - and since you don't think, you don't act.
So, the point is,
If something affect your senses, Freedom of Movement can't help you.
Think like a "Houdini Effect". Houdini can escape from almost anything, considering that he
knows what's going on. If you throw him with a concussion inside a closed coffin... well... he will stay there.
So, to determine what Freedom of Movement removes or not, use a simple rule:
Why I can't move?
If you can't move because a spell or something is hindering your body to move, like Web, Freedom of Movement can help you.
If you can't move because a spell or something is making your brain go gonzo, like Stun, or because your body becomes something that can't normally move, like stone from Flesh to Stone*, it won't help you.
*Flesh to Stone don't impede your movement, it merely limits you to the movement that a stone statue is allowed to do. A "Freedom of Movement"-ed and "Web"-ed person would become a completely untangled stone statue.
Also, read Freedom, the 9th level spell:
The subject is freed from spells and effects that restrict its movement, including binding, entangle, grappling, imprisonment, maze, paralysis, petrification, pinning, sleep, slow, stunning, temporal stasis, and web. To free a creature from imprisonment or maze, you must know its name and background, and you must cast this spell at the spot where it was entombed or banished into the maze.
Emphasis mine.
Freedom removes a bunch of effects, like Flesh to Stone and Stun. It would seem rather... strange to say that a way lower-level spell can do almost all the things that a 9th level spell can. Freedom is Freedom, not Freedom of Movement.
By RAW Freedom of Movement does, Freedom doesn't. Freedom of Movement ignores anything that would impede your normal movement, this includes encumbrance and difficult terrain. Freedom is very specific in what it frees you from however, not to mention Freedom is an instantaneous spell so it only helps you in the immediate. So even in the case of something like web, if you were freed and then immediately failed reflex again and got stuck, you'd have to cast Freedom again. Freedom of movement just wouldn't let you get stuck by anything as long as it's working.
Although you bringing it up in that case you could rule it that the squares of difficult terrain you're currently in turn into normal terrain, and that all your gear falls off. However that wouldn't be RAW, it'd just be funny.
Best Answer
Freedom of Movement explicitly disallows the application of two conditions to the subject of the spell, namely they can't be paralyzed nor restrained.
Stunned is also a condition. It is not listed under FoM as disallowed. Stunned also does not reduce the target's speed. It states that the target can't move, whereas other conditions, as you noted yourself, explicitly state an altered speed value.
The paralyzed condition is almost the same as the stunned condition, the only differences being that 1. a paralyzed creature can't even speak falteringly, 2. attacks targeting a paralyzed creature and coming from an attacker within 5 feet of the paralyzed creature are critical hits. Paralyzed inflicts another condition, incapacitated on the target. So does stunned. Stunned does not inflict paralyzed on the target. FoM explicitly disallows paralyzed, but it does not mention stunned, ergo FoM does not protect against stunned, nor against spells that apply stunned, such as Power Word Stun. Considering there's no Power Word Paralyze and no Power Word Restrain, this seems to be a conscious design choice.
I'm not sure I like this, but this is how I read RAW: FoM does not allow movement when its target is stunned regardless what applied said condition to its target (and no matter that stunned is a weaker version of paralyzed.)
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RAI I think the reasoning behind this is that stunned affects your mind, not your speed. Your speed is the distance the creature can cover. When stunned, its speed is the same, only the will to cover the distance unaffected speed would allow it to cover is impacted. (Also, the word "move" in the definition of stunned covers not just the movement of the legs or similar which allows the creature to go some distance. A stunned creature doesn't gesticulate, etc either. At least in my interpretation.)
(PHB 5e 1st printing, 2014, no errata, pages 244, 291-292)