Saying that you do not own your unique genetic code is not much different than saying that your ears, eyes or kidneys are not yours, and might be helpful form others, so anybody could take them. Think about it.
Is not so easy. A DNA chain is a physical object and information at the same time. If you copy it, you are copying an object that could be used to "make a copy of you", and allowing "random company or people" to pick this info opens the door to several problems. i.e. Imagine that somebody stole your sperm somehow and use it to make a child and blackmail you asking for money each month for 18 years because you are "the father", so pay me. Boris Becker suffered a similar case.
In the same way synthetic fragments of your DNA could be left in a crime scenery. It would be enough to clone only the handful of good parts able to trigger a rape test, and we have machines that could be feed with your public data and programmed to do this. No need to say that this could put you in a jail for the rest of your life, or worse.
You need to protect yourself from a lot of posible evil uses of your unique code, past and future.
Given that I literally gave half my genetic code to my daughter and she does not actually have any portion of my literal ears, kidneys, or eyes, I think you're overdramatizing.
That's a bit of a strawman. I guess people shouldn't donate blood with your line of thinking. It's apparently the same as donating an organ that doesn't replenish itself.
The blood that you donate is not taken for making a profit by a private company. Is strongly regulated and do not depends of the income of external investors expecting a profit. At difference of a private company, nobody will buy the goverment tomorrow.