First of all, before you start the company you are thinking about you need to get professional advice. You need a better understanding of these issues related to your questions.
I will however address one non-legal issue: while legal issues are involved in this topic, the fundamental question your are asking can be answered.
Why should the output of the R&D staff of a company belong to the
The company is taking the risks involved in this process. They are providing pay while the R&D staff works on the project. The company is providing benefits. They are renting space for the lab. They are buying computers and software. They are buying lab equipment, and supplies. They are doing this for months or even years, even if the idea doesn't work has they hoped for.
You ask in a comment:
So, how do MIT and Stanford students run start-ups based on their
They do so after negotiating an agreement with their university. When somebody pays for the R&D they get some level of ownership. That means if the funding is coming from a government agency, or from the University that funding organization may have some right to the IP. It depends on the terms of the agreement that is signed in advance.