The category you describe would softlock in Soda Jungle because the only way to advance out of Soda Jungle is either pull the Red Flag in 5-2, 5-4, or 5-5 to get to Iggy's Castle or pull the red flag in the Soda Jungle Ghost House to get to the Secret Level that shortcuts to Meringue Clouds. All the black flags in the levels I just listed above would eventually lead to a dead end.

Alternatively, there's a very unpopular category currently not on the leaderboards called "No Secret Levels" that does not do any of the secret levels to skip ahead of the worlds but it's too similar to All Castles with the exception of the fact that you can skip World 3 and you get to do 5-Airship. Currently I've been the only guy who has done that run and it isn't a very exciting run to see or do.

And even No secret exits were possible, the route is almost similar to All Castles (except you do some extra levels and you can skip W3 or 4) and it will be an unpopular category. Same for No secret levels like Mchan said.

So if you want to run the whole game, do All Castles or hundo