Unfortunately a lot of web developers are poor when it comes to implementing typography well.
There is a lot of typography that is frankly shockingly bad to be found. This is even the case on websites customers have clearly spent some serious money on.
Modern CSS and techniques such as Clamp should mean the type on website works on all screen sizes. Type also needs to have been set out with an eye to good structure, alignment and line length to work well for your visitors.
See masterful use of Typography at Pentagram the greatest design agency on earth. if you can afford to use them you won't be interested in me.