They must have really hit a nerve in you, eh?
Though the direction of the game doesn't indeed have role playing in mind, it wasn't unreasonable to assume that you will have a say in what your character will be in a game that was marketed as an RPG first.
Also, by your logic Bladerunner isn't cyberpunk because Deckard and K aren't punks?
Bladerunner is Tech Noir, not Cyberpunk.
While it has the "style" of Cyberpunk, IMO it lacks stuff the Cyberpunk book elabored on it (cybernetics, social decline, etc...).
Robocop IS Cyberpunk, you have ultraviolence, human stories, Corporate business, etc...
Robocop is a Cop, but the whole world has a big "punk" written on it.
Blade Runner, it's more like a nice tale with robots and poetic stuff into a cyberpunk looking world, that's how I feel it.
Cyberpunk isn't much about how it looks but the feel of it, in Robocop you really have that crazy city, that you feel is about to explode, rampant crime, etc..
While in Blade Runner, even the new one, I dunno, it feels more like psychological dark scifi in a future world than Cyberpunk, I wouldn't mind living in Blade Runner's world honnestly, it's not that bad... Robocop's one? Well.... Maybe not....
They barely talk about social or politic stuff, it's all a poetic thing on human and stuff, Post-Cyberpunk maybe, but not "Cyberpunk" at the classic meaning (like Max Headroom that the whole point was to criticize media etc..).
To me Aliens 2 is more Cyberpunk than Blade Runner, you have future tech, corporates agent trying to fuck up the people they sent to a mission, and they all do feel "punk".
Strange Days also, really do link it's scifi feel with some social and politic comment about society's collapse, espace using drugs and police brutality.
Blade Runner, it's about a detective falling in love with a robot, it's not more Cyberpunk than I robot or any movie like that, if you remove the background scenery.
While I do love Blade Runner, I think it was a good inspiration for how Cyberpunk evolved, but it doesn't represent it as a whole (which is just my 2cts anyway).
Now, there are plenty style of cyberpunk (if you compare Gibson/William/Spinrad/Sterling, etc.. way of writting cyberpunk, there's tons of differences), but some stuff remains in the genre
Anyway, back to the Corporate.
There are actual supplements for the Roles in Cyberpunk 2020, and how each corporations behave, and yeah, on paper you can create stuff on the fly to make it interesting (and give a reason for one of your player to BE the corporate), but working it on a videogame would be challenging, they're just the perfect bad guys.
You have a corporation that the CEO just killed another CEO and his daughter (and actually enjoyed doing it) only to get his corporation without having to sign a contract and spend any money, I mean, that's how those guys works in 2020 and most likely in 2077, they went on a Corporate Wars and destroyed blocks of a city just because they can't stand each others.
Imagine how people see them, those massive corporation are monolithic and don't give any credit to people's lives, that's just how they are (and what I tried to flesh out, not having some nerve thing).
Playing a corporate (mostly high-end), in Cyberpunk standards (the RPG, not the genre obviously), would just kill the "player choice", since you're just a tool in the corporate chain, and everything you do etc... is monitored
(the "they put bombs in your body" wasn't a joke...).
That's why playing a "Punk" or "Mercenary" is mandatory there, you'll have your choices, lots.
Corporation uses mercenary for their dirty job that they need to do outside of the Corp spectrum.
It lets you works for a corporation, but not having to deal with it's inner-rules.
Working FOR a corporation lets you no choices and a boring and repetitive life, it's just how the game depicts them.
Imagine watching Matrix, but Neo would just be like "Lol, hell no" at Morpheus and would do his job for 1h30 behind his desk, that's kinda how it would feel playing a corporate, it's super strict.
To be a bit more clear, the more you go up the corporate ladder, the more of a psychopath you are
(because you stab more and more people in the back to advance yourself; IE why the corp told V "Accept to fuck people over and in a few years you'll be where I am, so yeah, not like they're the nicest people to hang with), if you follow the hierarchy and autority, you'll won't move, if you fuck people's work and put the advantage to yourself (like hiring a bunch of punk to fuck your coworker works and have the spot for yourself), that's how you got up the ladder.
I tried to flesh the feel of it, not because corporate are just assholes, but because the game, as a corporate would just feel as fun as doing photocopies for 3hours, and trying to screw your coworker job, just that, while working as a freelancer actually offer way more freedom as a player.
Also, being that much of a high-end assassin would be limited "lore" wise.
The people up there have most probably stabbed people tougher than you in the back and probably will see you comin' way ahead (they're not there because Daddy promoted them up), and if YOU want to get to the upped ladder, it'll just block you in term of Roleplay (you'll stick to the corp standards and that's it, since you're blocked in the corporate way).
I dunno if it's clear, but that why playing a "punk" is easier, you have more freedom, which doesn't stops you from working for a corporation and liking it, but you keep away from all the "blocked acces" being into a corporation would put to you (goodbye combat zone, drunk night at the afterlife, etc...), you'd life your yuppie life, wich would be kinda limiting given the world's size
(and because it's how it works in a corporation, if you don't fit, you don't stay, so they're all like-minded etc..)
I can't lie that as a DLC, that would be really sick.
There are corporate buildings, there are apparently a way to explore those buildings, I wouldn't be surprised if you'd be hired in different corporations over the game's story, having to do shitty job from the other side of the mirror (as the corporate asshole), but you'll eventually get back as a punk in the street, just to keep the "freedom" of doing whatever you want.
Like, you won't go work to Militech if you're stuck as an Arasaka corporate, reason why the "punk" role is important, there you can do whatever you want, be a nice guy or thinking that being a corporate dickheads sounds nice (and honnestly, I'd love to do a character like that, American Psycho style)