Text shadows can make text pop but do not make text more readable.
I'll concede that adding text shadows around white text on a white background will make the text more readable since anything is more readable than invisible. I disagree, however, that using text shadows around black text on a white background is more readable than simply black text on a white background.
Proper contrast is the key to readable text
If you want the text to stand out because it is special then adding text shadows can accomplish that. If you are just trying to have the most readable text, however, then high contrast without text shadows is the way to go. For example, some version of black text on a white backgroundblack text on a white background.
If you know the environment is going to be a dark server room or something then the server room guy will thank you for using some version of light text on a dark backgroundlight text on a dark background.