1. Companies sometimes fund research groups to get the benefits you've listed
Perhaps a company would be interested in fully funding your M.S./Ph.D. only if
you put their name at the top of all your published papers.
any patents that come out of your research are owned by the company
When a company wants advertisement through publication or patent rights, they'll tend to fund a research group instead of an individual student.
In turn, the group typically claims their corporate sponsor in publications and often focuses research on topics that the sponsor's interested in, including sharing intellectual property rights.
This doesn't really work when a student's funded directly. For example, most schools tend to claim rights to their students' inventions, which would prevent the students from being able to pass them to their employer (at least simply). Additionally, there's little reason to have someone who's already an employee go to grad school to get 'em to do research; R&D departments can just do it directly.
2. Reasons to pay employees' tuition
Tuition reimbursement's primarily synergistic, motivated by an alignment of interests.
This is, if you pay for an employee's tuition, that's a huge perk for them, and thus part of their compensation - kinda like health insurance and other benefits are.
And like other benefits, you might provide them to an employee instead of just paying the employee more because there's some sort of synergy. In the case of education, it's often that you want educated employees, and by educating one who's already in-house, the result is an educated employee who knows the ropes and is invested in the company.
There're more factors involved, but they can get pretty situational.
3. You can probably negotiate this benefit with many companies
If you want to go back to school, you're asking the company to incur a cost. So just like getting a pay raise, you'll want to show them that it's in their interest to give it to you.
Hypothetically, say that you're about to leave the company and don't want to have to agree to stay after your education's complete. Then, how do you make that worth their while? That might almost require you taking a pay cut approximately equal to the tuition. And it might even be worse, since you'll basically be telling your employer that you'll be distracted with a side-job (school) and then leaving the company soon.
On the other hand, say that you're a great employee and you want the company to fund an MBA done in weekend classes so that you can move up to management; further, you agree to stick around for at least 10 years after finishing the MBA. That's a far more attractive offer, and a lot of companies would go for it. Many already offer such options.
In general, you basically just need to discuss it with an employer like any other sort of arrangement.
Found a great article with advice on this topic: "How to Ask Your Employer to Fund Your Education", Investopedia:
Discussing Education Funding With Your Boss
Pick your degree/diploma or designation/certification
Pick your course(s) and your school/college
Create a list of ways your company will benefit:
You will add new skills to the workforce.
You will be more productive and therefore able to increase company revenue.
You will be able to take on new assignments and generate additional revenue.
You will be able to take on a leadership role within the company.
Your degree/diploma will present a more professional image/give prestige for the company.
You can mentor new employees and spread new skill sets to other employees.
Anticipate questions or concerns that your HR manager might have. Try to answer questions in such a way that your answer leads back to a benefit for the company.
Concern: time away from work. Response: night classes or online classes will fit into your free time, which will add new skills and increase productivity.
Concern: company expense. Response: tuition may cost less than hiring and training a new employee with the degree/diploma/certification. Your education will make money for the company.
Practice your Q&A and be prepared. Take your notes with you into the meeting with your HR manager.
If your employer refuses, don't give up. Try again next quarter.
-"How to Ask Your Employer to Fund Your Education", Investopedia