Maybe this is not an answer and maybe it doesn't apply to your application, also you don't clarify if it's a desktop or mobile application. When there are shortcuts I guess is a desktop app.
I only tell my experience about the existence or not of buttons.
QuarkXPress is a text editing program that in its first versions the most important options were achieved through keyboard shortcuts. Many of them had their corresponding option on the menu and others did not. At that time I wondered what was the need to have the menu option repeated when the keyboard shortcut already existed: more comfortable, more immediate, more user friendly. Especially in editorial design, whose speed of execution requires the use of both hands to accelerate the process.
Until one day I had to teach how to use QuarkXPress to a large group of students with paraplegia in a hospital training center. No keyboard shortcut made sense, they were all totally useless.
The user with mobility impairment has a special mouse, a hemisphere that allows him/her to move around the screen and the click options are through pressing the sphere.
It was a nightmare for me to reinterpret a whole very complicated application with all its menu options and tool buttons. But nothing compared to these students and anyone who needs to activate an option with some motor impairment, specially when it doesn't exist.
Perhaps in the analysis list you should include people who cannot use keyboard shortcuts, which is also a market and quite numerous market knowing their life is quite sedentary.