I mean, I don't really care to optimize "number of buttons per screen" (and text can be as dense as it wants, although I usually set my font size to 16pt or above) but to each their own.
The relevant cost of too much padding isn't fewer buttons on the toolbar. It's that too little of the screen is actually showing me the web page I want to see.
It's usually most important to quantify in the vertical axis; today's bloated touch-oriented UIs are horrific for 16:9 wide screens. Add up the taskbar, window title and tab bars, URL toolbar, the 72pt dickbar menu at the top of the web page with single-line labels, and the cookie banner at the bottom of the web page, and you're lucky to have half of the shortest dimension of your screen devoted to real content until you start excising the bad UI elements. It's like being back in the 1990s and seeing the old horrors of people who said yes to every adware toolbar that asked to install itself, except we're now wasting far more vertical space for far less functionality.
It's usually most important to quantify in the vertical axis; today's bloated touch-oriented UIs are horrific for 16:9 wide screens. Add up the taskbar, window title and tab bars, URL toolbar, the 72pt dickbar menu at the top of the web page with single-line labels, and the cookie banner at the bottom of the web page, and you're lucky to have half of the shortest dimension of your screen devoted to real content until you start excising the bad UI elements. It's like being back in the 1990s and seeing the old horrors of people who said yes to every adware toolbar that asked to install itself, except we're now wasting far more vertical space for far less functionality.