Any character with great mobility (speed of 40 or 50 ft or more) needs to be considerably more fragile than the slower counterpart.
Including melee characters? Once they're toe-to-toe, that extra move isn't going to stop them getting hit.
Any character with great range (more than 30 ft, definitely) needs to be considerably more fragile or at the very least severely disadvantaged in melee.
You might want to clarify this. I can't off the top of my head think of a single player character, even a melee-focused one, who didn't have a range option better than 30ft once they had opportunity to pick one up. Even if it was just a dagger or javelin or two.
Even outside of a game with my houserule allowing either Dex or Str to be used with bows, many melee-focused fighter-types carried longbows.
Now, I hear you saying "but the game DOES give tanky shield fighters the highest AC in the game". Problem is, even ranged fighters get enough AC.
5th edition is sufficiently easy that you never need that extra boost of AC. Once you have AC 18, you're fine. Getting to AC 21 already at low levels is overkill.
On the contrary, due to the bounded accuracy, increasing your AC from 18 to 21 very significantly reduces incoming physical damage. More than the step from 15 to 18 AC will for example.
Not to mention counter-productive. After all, there aren't any real "stickiness" to D&D tanks, no aggro mechanism for instance. So if one of the heroes sport an almost-impossible AC 21 maybe the monsters simply attack somebody else..., especially if AC guy is slow and immobile? Which would be completely opposite why the fighter put on his armor in the first place!
I would imagine that most fighters put on their armour in the hope that it would stop them getting hit. If its working, its not the opposite reason.

While they only get one attack of opportunity a round, few monsters intelligent enough to recognise their chances of hitting the heavily-armoured character want to be the one to provoke it. The situation however, also can contribute to this. If the DM runs a lot of encounters in open plains rather than cave systems, buildings, forests or urban areas for example, the setting can affect the most common tactics adopted by both sides.
Let me say straight away I won't argue for a return to the days of 20 ft Speed in heavy armor. I fully understand why that was scrapped - it IS overly frustrating to have no less than 50% less speed than the "norm".
What is the "norm" and how was it determined?
Based on my observation that none of the Fighters go Strength and Heavy Armor (precisely because Dex + mobility + range is so superior), we probably need to take down Light armor a notch but perhaps not Medium, since we've already concluded a min-maxer will choose either light or heavy: going "in-between" never leads to optimal results, and medium armor is probably only optimal for the Barbarian and that's a special case.
Where was that observation made, and what was the sample size? IIRC a single run of OotA is probably a bad sample set because the situation and environment encourage stealth and make it quite hard to obtain heavy armour.
a) remove Studded Leather entirely
I support this.
I would love to increase Shields to +3 or even +4 to properly compensate for the loss of versatility (no two-handed weapons like greatsword or bow)
I'd certainly support this idea from a realism standpoint.
Based on my observation that none of the Fighters go Strength and Heavy Armor (precisely because Dex + mobility + range is so superior),
I don't disagree. I am well aware not everyone makes characters based on optimisation reasons.
But that's not the topic here
No, but it seems to be a claim that you have made.