Some people need extra help surfing the Web. Some use readers to actually read the content of a web page and others need to enlarge the text of websites using Tools >>Text Size. When your web designer creates your page design and uses a pixel size for fonts instead of a percentage or an em, you are defeating the ability for readers who need extra help to get it.
As a web designer myself I do like to have control, but now there are many new options that designers and site owners simply need to be aware of to help. One new option is to use a global style sheet that controls your fonts, font sizes, colors, and links all on one page for the entire website. Another one to be aware of is to describe font sizes in a percentage or as an em, which is the width of the letter m in any font. Using these font descriptions instead of using a pixel width description allows your reader to resize the font as needed.
Web designers need to design especially for use of font accessibility, it is not something that can be added as an after thought but rather as an integral part of a new design.
I am currently in the process of redesigning my 1221 page website and am incorporating improved accessibility features in my new website. So when you hit a website where the font doesn’t change even when you click largest font, you will now that the web designer has defeated one of the biggest tools on the Web that shouldn’t be tinkered with to help people who need it.