Why don't we get the root key for "our" android? I know what root is for and how to use it etc. but I'm always wondering why don't we get the key for root access for our android phones? Why won't they add an extra sheet to the box with the key so that it doesn't have to be hacked or make it possible to request it for advanced users?

If I bought a phone why can't I use it freely?

Can somone explain the rationale behind this? 

Is it a legal matter or just you are too dumb to use your phones and we want to protect you from yourselves?.

On Stack Overflow I was told it's an opinion based question but how can it be opinion based? There must be a reason why they won't reveal the root keys. I'd like to know why they made this decision rather than what you think about it which then really be opinion based.
Security - imagine someone got hands on bunch of those keys for root access. It would be your device that someone else freely controls. Someone connects remotely, takes all your data, makes a huge bill or just destroys your phone - and the OEMs say it's not their problem that you got hacked, this is not their device anymore. Imagine blaming the WiFi card manufacturer because you were hacked online.

Basic users - they don't want to think about or even know how to secure their device - they expect it to be secured by the OEM and that all is taken care of.

Profit - some devices cost less than or equal to their production cost (like PlayStation) and OEMs rely on purchases you do through their services to make the device itself profitable. By allowing you to easily remove all their services you deny them their expected income, otherwise we would pay double the money for todays devices.

Bussiness - there's a reason that bussinesses use highly secure devices, firewalls etc. A phone that comes with a key that bypasses it all won't really sell in those circles.

I don't want to say that I don't agree with you, and I would also love some easy way to root and use my device however I want it, but there are so many reasons why such a thing shouldn't be done.

If you want something like that, you can use an HTC or Sony device (you can request a bootloader unlock key) or you buy a development device, that is not for mass production, but for developers only, but of course, they cost way more and are harder to get.