Do you think entrepreneurs will pay for a membership site about the psychological aspects of business ownership?

I believe you can build several products around that niche and sell, like ebooks, accountability programs, coaching etc and use the psychological aspect as the axis around which you create the content to promote those products... so may be a blog which consistently educates and inspires on such topics but also has some info products and coaching etc for those who need more support. Otherwise building a membership site only on the content is a bit tough now a days because some super good quality content is available on almost any topic for free or almost free.

On that note, I used to blog on somewhat related topic almost daily and have not done so for over a year and still get a few sales every week on the book I have on that blog. If you'd like to chat more about how I built it and market it on a shoestring budget, I'd be happy to help.

Thank you all for your excellent answers. I'm trying not to sound negative, but in marketing they say "where is the pain that you can solve." I'd love to hear more feedback.

It's a very good idea.
The worst things about a business aspect is to add makeup to fake the truth. The negative list you mentioned are the real pain every startup will face as well as well established businesses at some points. The difference between startups and well established businesses in this regard is that the second can hire coaches to solve such problems. I assume that your platform can create an intermediary way to offer businesses at any level the solution they need for the problems they face.

Identifying the real pain is the first step toward success. Therefore, you are not teaching entrepreneurs how to be stressed but you're giving them solutions to reduce stress.

I think the idea would be very helpful if you offer phone coaching or skype beside articles and videos.... Entrepreneurs are very busy people, and it's hard for them to spend time in reading documents only. Sometimes they need immediate help (reading will not be an option for them).
Entrepreneurs like to measure progress, for that you need to offer them outcome measurements for the progress of their efforts on your platform.
Later on it's better that your platform connects mentors in those fields and potential entrepreneurs who are in need of such services.
We live in a very fast paste entrepreneurship environment. Entrepreneurs are more willing to participate in platforms that give them higher results in a short time period. For instance if you offer video coaching make them short and toward the point. A great video coaching you can find on youtube is for "Evan Carmichael". They are short, follow three points solution pattern and toward the point (the longest one is 5-7mn length). If you need longer time divide your videos into steps solution.

Remember that entrepreneurship becomes a lifestyle in business and careers. Today, Companies tend to hire employees with entrepreneurs skills and not old fashion employees. You services are ideal for business owner as well as for their employees.

Happy to talk to you in more details by phone.

Here's an pretty reliable way to test ideas like that.

First, are there competitors already in that space? There should be at least a dozen because that indicates viability. You might very well be the first to succeed, but the odds are against it.

Second, are people losing sleep trying to find the solution you are offering? You want that sort of marketing power or the spend moves from the "need" to the "want" column.

Third, save up all the money you'll need before you launch. Debt is the modern equivalent of slavery and it's just too easy to think you have a great commercial idea when people are throwing money at you. And you aren't allowing natural market forces to tell you that's it's not a go. How serious, committed, and disciplined are you? Save it up. You'll spend it a lot more carefully, too. :)

Fourth, don't start anything without an exit plan, even if it's provisional. Address when you'll fold up the tent, too. Stopping takes as much courage as starting, and it's the TRUE mark of an entrepreneur. It's the stupid people who keep going when they shouldn't.

Fifth, spend a lot of quality time articulating your positions on this topic. Fill your head with ideas like you've done to this point and you won't gain much additional clarity until you empty your head. Besides, the clarity comes IN the articulation.

Best wishes to you.