Ever thought about marketing a dragon's enormous skills, especially on the magical sector? No? Think about it
Magical competence is rare and therefore expensive in the Sixth World, and a character starting out with a magic attribute of at least 6 (max. 10) may earn one hell of a money for financing his first steps...

Sure, I've even suggested that a relatively easy way for a new dragon to earn some extra cash is to contact the local Talismongers, "For a limited monthly fee, I'm willing to fill that cup with whatever you want."
But if you look at the rules, the starting Dragon character DOESN'T have enormous magical skills. He's going to fit in pretty much equally with other starting characters. No centuries of practice, no world ending spells, etc etc. Sure, depending on how you arrange it, he might be slightly better than a street shaman, but it won't be by much. And then we're back to being owned by the corporation
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Sorry, but comparing a dragon to lab rats is simply ridiculous. Yep, a dragon may run away, if a corp makes a stupid effort at what you described. Wouldn't be the first time that a dragon "broke things", would it?
I agree that a dragon might want to take precautions when approaching a corporation. I also agree that the corps may force their employees to do whatever they want. A dragon, however, is none of your typical sararimen to be tossed around. There are also "confirmed stories" about corps drooling over getting their hands on awakened personnel. I am sure they would rip their fingernails off for getting a dragon into their ranks as an astral defense or security adviser. And what is the use in destroying that magical potential by implanting cyberware? (Which, by the way, is only one of many sectors of the market that not every corp covers; we're talking about A corps and below here, concentrating on on only one or two sectors, not about AAs or AAAs. I agree with you that running directly into the Paranormal Research Department of a AAA might have some... unpleasant consequences)

But we've already seen it. Atleast one Dragon has been scooped up by a corporation and had cyberware implanted into him against his will. And you still seem to be operating under the assumption that this is a Great Dragon or something, or a character that's massively more powerful than any other starting character, and for the most part, they aren't.
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Once more, you compare dragons to mere (meta)humans (better this time than the lab rats, though). Humans are the standard in the Sixth World, and it is usual for them to run the shadows. Any way you look at it, dragons are not like this. They're rare and therefore special. And for them, running the shadows is even more special. With placing them in the shadows, you do something pretty unexpected, which is fine - as long as you justify it well.
And? Again, I've never suggested that a Dragon doesn't need a good reason to run,and that a PC dragon doesn't need a good reason. I've said exactly the opposite. I've merely stated that as a fictional character, I don't need to know Tessien's reasons for running. He's not in my game, he's not my PC, I don't need to know his motivations. Just like I don't need to know Hart's, I don't need to any other Prime Runner's reasons, I don't need to know what the motivations of the original Sullanciri, I don't need to know the motivations of "The Merlin" from Dresden fame, nor do I need to know what possessed the Dancing Joker to do what he does.
Its only when someone sits down at the table and says "Here, this is what I want to play," that the motivations and reasons behind the character matter to me. And the rules give them the chance to do so, so having the rules and the options is perfectly fine. Its not some license to say "Well, because I'm a dragon I don't need to have a background or motivations," or "Because I'm a dragon I don't need to answer the 20 questions," etc. Its not even some magical Red Line that's going to ruin Shadowrun. Its simply another choice in a game that has many.