These API URLs are completely static and side effect free. We considered using a POST body, but then would lose CDN caching, which would make a difference at xkcd's scale. We also decided that URL length restrictions would not likely matter for real world morse input.

I hadn't considered using a query parameter -- that's a really interesting idea! That seems like it'd have been a more elegant solution than the special cased padding we ended up with.

Especially for static/idem potent resources where URL length isn’t a concern this is exactly the kind of thing query parameters were designed for. If you do revise it to adopt that please credit Roy Fielding :)