Whenever I visit a tag info page, I find that the tag-excerpt is hidden by default and there is a link called "show excerpt" at the bottom. Clicking this causes the excerpt to appear at the top.
Why are the tag wiki excerpts hidden by default?
The only way to get to a tag info page (other than editing the URL) is by clicking a link
Learn more that is shown by hovering over a tag (or clicking
Info on [site].stackexchange.com/tags). This is because it is expected that you land on the tag info page because you want to know more about the topic/tag after reading the short, concise description (ie. the excerpt).
The main tag wiki should stand by itself - if it needs to refer/rely on the excerpt to make sense, it should be edited to remove that dependence.
There isn't any need to show the excerpt by default - it would just be a waste of space, because it is, in effect, useless once you land on that page.
The default info page is the tag wiki, which has more info than the excerpt.
The excerpt is a brief summary of the wiki, so it makes sense to show the wiki by default, which is the full info, rather than the excerpt.
Excerpts are mainly used for providing info when you hover over tags around the site, as they are a smaller "summary" of the wiki and so fit better within small pop-up boxes.