Accessibility - you can't search Twitter for Alt-Text

Twitter has recently improved the accessibility of its site. When uploading an image, a user can add alt text - a short description of the image for people with visual impairments.

Here's an example:

Terence Eden is on Mastodon

@edent

This is a test to see if alt-text in images is searchable on Twitter.
alpaca omnithorp pic.x.com/jhgcsaxpkd

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If you take a look at the HTML source, you can see that I've added a unique string as the alt text. That should make it easy to search for.

If I search for the text of the Tweet - Twitter finds it without issue.

But if I search for the unique phrase in the alt text?

Nothing!

Here's my question - should it?

Twitter has an impressive advanced search function - allowing filters by sentiment, date, location, and language. So why not search by image?