One way to solve the problem of the text to look good on both desktop and mobile/tablet is in fixing the text size to physical units like physical centimeters or inches, which don't depend on the screen PPI (points per inch).
Based on this answer, below is the code I use at the end of the HTML document for a responsive font size:
<div id='testdiv' style='height: 1in; left: -100%; position: absolute; top: -100%; width: 1in;'></div>
<script type='text/javascript'>
var devicePixelRatio = window.devicePixelRatio || 1;
dpi_x = document.getElementById('testdiv').offsetWidth * devicePixelRatio;
dpi_y = document.getElementById('testdiv').offsetHeight * devicePixelRatio;
function setFontSizeForClass(className, fontSize) {
var elms = document.getElementsByClassName(className);
for(var i=0; i<elms.length; i++) {
elms[i].style.fontSize = String(fontSize * dpi_y / 96) + "px";
}
}
setFontSizeForClass('h1-font-size', 30);
setFontSizeForClass('action-font-size', 20);
setFontSizeForClass('guideline-font-size', 25);
// etc for your different classes
</script>
In the code above the items of a different class are assigned font sizes in physical units, as long as the browser/OS is configured correctly for the PPI of its screen.
A physical-unit font is always not too large and not too small, so long as the distance to the screen is usual (book-reading distance).