I want to install a plugin using wp-cli (or anything else) on a WordPress based website. I have URL, admin-user, admin-pass only. (no FTP/ssh). I want to do it programmatically, without going into the browser. I am able to do so on my local WordPress install.
At the risk of stepping into the unknown, I reckon that you are over-complicating things-full remote access to the WP database sounds like the most effective solution. What could you not do if you had access to the database?
Having said that, you have a duty to have done your own research, and to have explained what you have tried &/or how you have approached a solution. For instance, have you looked at any of the free and/or “open source” solutions (the five minutes I spent on research revealed “MainWP” or “Shift8 Remote Management” as possible candidates). I sense that you have come in search of the holy grail, and while people are only too happy to assist you, there is no such thing as a “free lunch”.