The "alt" tag is meant to show text when the image isn't loaded, the "title" tag is meant for a description of an image on cursor hover. IE has been doing that wrong for many years, where Firefox follows W3C standards. A properly coded webpage should have both "alt" and "title" tags.

It is not so much IE was doing it wrong they were using ALT before there was a standard for that and before there was a TITLE on images but IE9 does show title

• https://support.mozilla.com/en-US/questions/838888

If titles do not show up on tooltips

• https://support.mozilla.com/en-US/questions/860902

• Popup ALT Attribute: https://addons.mozilla.org/firefox/addon/popup-alt-attribute/

Unfortunately, after checking into the W3C, the alt attribute in the IMG tag is required to pass XHTML specifications, but the title attribute by itself in an IMG tag will not pass. Doesn't it make more sense to use one tag (that passes XHTML) for "alternative text" than to have to use two that across browsers does the same?

You need to use both.

The alt text is used if the image can't be displayed and the title text is used to display a tooltip on hover.
Both have different purposes.