@tizianopiccardi has extracted this data for January 2021.
Captions on English Wikipedia
If we exclude all gif, tiff and png images, English Wikipedia has 7'811'234 images. Among those, 3'645'913 have a caption: 46.6%.

Alt Text on English Wikipedia: TO DO
We are working on getting the alt text statistics. A first inspection showed that most "alt" field are populated with the image name, e.g.:

<img alt="Osaka07 D6A Betty Heidler Medal1.jpg" src="....
<img alt="Alfred king of Wessex London 880.jpg" src="//....

Tiziano will give me a list of alt text fields and I will work on filtering out these cases so that we can have a reliable estimate.

Beyond English Wikipedia
Due to the many formats/templates used to add images and captions via Wikitext, to extract this information, we are relying on the pages' html. We have html data available for English Wikipedia only for now. Unless we have a better system to extract captions and alt text, extending this analysis for other Wikis will require quite some time, as we need to download the html for all articles in a Wiki. Any help is appreciated!

I would be happy for now to just have the information for English Wikipedia. Thank you very much for your help so far.

Here some additional stats for English Wikipedia:

• 52.1% of the images have a non-empty alt text
• 27.0% of the images have a non-empty alt text AND not ending with .jpg, .jpeg, or .png

For this remaining 27%, the quality seems not particularly curated and informative. By looking at random 20 non-empty labels, I noticed cases like 'Refer to caption', or 'A younger man and an older one confer together.' for a picture of John Kennedy and Khrushchev.

I uploaded the dataset here: https://drive.google.com/file/d/1qmz-DHbFjEicwzEWDaSMGTEbW_smLbQq/view?usp=sharing

Make sense, thanks @kzimmerman !