Thanks for trying to do things right.
My primary complaint is the astronomical prices and extortionate business practices of some publishers. For example, The Cost of Knowledge is a boycott of Elsevier with over 20,000 participants (I am one), by researchers who object to their practices. I recommend that you read their statement of purpose, signed by world-famous mathematicians including multiple Fields medalists, and avoid the practices which they object to.
You mentioned MDPI. I reviewed a paper for them once, and I will never have anything to do with them again. They made ridiculous demands, such as a referee report within three days -- totally out of line with what is expected in mathematics. They also have spammed my inbox repeatedly. Please do not do this.
Another complaint is that copyediting can be terrible. There is nothing worse than to pour your heart and soul into a paper, submit it to an expensive journal, and watch it get mangled by careless journal staff.
You should keep in mind that academia varies more than you think it does; common publishing practice in one field will be totally unheard of in another. Researchers will not adapt to you; you will need to adapt your workflows to the customs and conventions of each field in which you intend to publish.
Finally, accept that as a publisher you will have little influence. For example double blind review is a very interesting idea, with very compelling arguments in its favor. Math doesn't currently use double blind review (with some exceptions), and there are significant drawbacks as well. If this changes, then it will be because prominent people from within the profession pushed for it. So by all means push for changes you would like to see, but push gently, and don't expect all of your initiatives to pan out.
Good luck to you!