The opening crawl is one of the most distinctive feature of Star Wars films. But only the numbered episodes have it, not Rogue One or Solo which are also part of the Star Wars franchise.
Why is this?
As you mentioned in your post, only the numbered episodes have it. Only the ones that are part of the main series, that is. From ScreenRant (a fairly reliable source for media), we get this:
While the opening crawls have been a part of every mainline Star Wars movie since the very beginning, Lucasfilm decided to go a different route with Gareth Edwards' Rogue One: A Star Wars Story in 2016. That was Disney-owned Lucasfilm's first Star Wars anthology movie, so to differentiate the flick from the saga episodes, the studio opted to start the film outright and then show the logo (which was also changed) after the opening sequence; Rogue One didn't have an opening crawl. Something similar happens with Solo: A Star Wars Story, though a key difference between the two anthology blockbusters is that Solo: A Star Wars Story actually has an opening crawl, just not a... traditional one.
According to Gareth Edwards (one of the directors):
The first screenplay that Gary Whitta wrote had a crawl in it -- and you learn doing that that 'a long time ago in a galaxy far, far away' has four dots in it, not three. You get extra marks for that. And then at some point, probably like six months before we were filming, we were in a meeting, and they talked about not having an opening crawl, because these are standalone films, not part of the sagas.
The directors of Rogue One originally had a crawl in the beginning. However, as mentioned by CinemaBlend (another trustworthy source for this information):
Eventually, Lucasfilm decided not to include one, apparently because they felt that since the plot of Rogue One: A Star Wars Story was born from the original text crawl, it shouldn't have its own. It did open with A long time ago, in a galaxy far, far away....
The crawls have a purpose, which isn’t applicable to the anthology movies.
Star Wars aped the movie serials of the 1930s and 40s, some of which opened with moving text that summarised what led up to the previous episode’s cliffhanger. The Star Wars crawls make us feel like each movie is an episode in a serial — and that we’ve missed some episodes in between the movies, as the crawls don’t generally recap what happened at the end of the previous movie.
Like the serials would generally focus on one set of characters, so the Star Wars movies focus on the Skywalkers and their allies and enemies. Rogue One and Solo are both adjuncts to that narrative; even the former, which shows us events leading right up to A New Hope, is telling the story of some other bunch of heroes in the Rebellion, not the Skywalker clan.
As such, they’re not part of the same linear narrative, so they don’t need a crawl.