I think it's definitely an issue with Rein if it's a common belief that the rest of characters in the entire category are not considered real Tanks, that is a mindset that is entirely skewed by the existence of Rein. It doesn't help that the only real character that can contest him head on is another Rein. He perhaps does not need a change in his kit, but he definitely needs something to exist as a true hard counter to him.
Are you sure this belief isn't founded in some truth, though? Because it seems like Blizzard's definition of a tank is "dude/dudette who has twice or more the health of the standard 200".
A tank's role in basically any game is the following: Stand between the DPS of both sides, preferably with some way to draw fire, soak up damage and protect the less sturdy teammates from it, and provide some way to set up the DPS in the team to make it easier (usually in the form of CC). Obviously, this means that tanks usually are also built to endure more punishment than other classes.
In other words, tanks are a support class first and foremost, just that their type of support is very specific (protect and CC), while other supports often are built on healing or status effects.
Now, Reinhardt does all of that. He has the health and his shield to soak up damage. His shield is so big that it can blockade chokepoints and protect big areas (i.e. he draws fire). And his ult is heavy CC, in which he stuns people in a cone in front of him. The charge is mostly a mobility option to allow him to get back to the frontlines faster (even though it can be used offensively), and the firestrike is a tool to scatter enemies, or get a bit of ult charge faster.
Let's look at the other tanks.
Roadhog's only way to draw fire is because he's so big. Otherwise, he is built like a self-sufficient, beefy DPS. At best, you can consider him a Tank-DPS hybrid, but all of his tools are made to do damage, except his heal which is a replacement for the mobility/escape options that other actual DPS characters have. He just heals the damage he took instead of running away. For all intents and purposes, Roadhog is not a tank.
Zarya is by far the closest to be another tank. She can protect teammates (and herself) by mitigating damage, and her ult too is very powerful CC. However, her ability to protect her allies is, compared to Reinhardt's shield, extremely short. She also cannot reliably draw fire, especially since she has a small model and hitbox. I consider her to be fantastic as a secondary tank and DPS, because while she doesn't excel at either, she is solid at both damage and the support that tanks do.
Winston, in certain team compositions and maps, is capable of tanking - he has the bubble and his big hitbox to draw fire. However, he clearly is not built to be a tank. He's by far the most fragile of all the tanks, and actually requires support from his team to be effective, because he is built to be a harasser. He jumps in, causes disarray and jumps back out (if he survives, which in good teams he should do). That's why his jump is on such low cooldown. That's why his weapon locks onto multiple targets but doesn't do a lot of damage. That's why his ultimate has him turn into a big angry gorilla and knock people around even though he doesn't do much damage with it. And while his bubble can be used to protect allies, its intended function clearly is to extend Winston's survivability as he jumps into the enemy team.
D.Va is in a similar boat to Winston. She is built to be a harasser, flanker and counter-flanker. In particular, her role is to pick off high priority targets in the backlines - healers, snipers, Bastion. She flies past the frontline and starts mowing the backline down. Her Defense Matrix can protect allies, but it's size is extremely narrow, so it's mostly there to protect -her- from incoming damage while she waits for an opportunity to jump the opponent. I guess you could argue that her ult is an indirect CC by causing people to run and try to take cover, but ehhh.
So if you look at those characters, only Rein ticks all of the boxes. He has everything that makes a tank a tank. And not just high health.
Funnily enough, closer to being a tank at this point is a character who isn't even considered a tank by Blizzard: Symmetra.
She has the ability to protect and draw fire with her shield and her sentries. Her ultimate while not providing CC can be used to either give everyone a massive mobility upgrade (down to the point as potentially working like a revive) or protect them even further by increasing their health substantially. The turrets also give her map awareness and have a slow effect, making them essentially her version of CC - an enemy that's in a carwash of 3 or so turrets is slowed down significantly and thus much easier to take out.
I still don't think she's a tank (more like a tank-support hybrid), but she certainly is better at fulfilling that role than fucking Roadhog is.
Oh also, there is a hard counter to Reinhardt: Bastion. Bastion just utterly and completely shreds Reinhardt's shield to pieces. It's gone within seconds upon continuous fire. And Bastion currently is a lot better on PTR (plus the change to spread on his turret mode doesn't matter when firing at Rein's massive shield hitbox).