The problem is we're comparing Appleseeds to Oranges. Appleseed is fundamentally structured as a educational organization. It's there to teach riflemanship, especially for new or amateur shooters. Its downside is that it only has one grade level - you go from cook to rifleman, and that's it.
If you want to get into competition, there are LOTS of competition offerings out there, from CMP/NRA to IDPA/IPSC to the casual matches at your local club (MRA has rimfire matches, which are close to what you're asking for above). But ALL those competitions are set up as competitions, not educational organizations.
If you show up to an Appleseed, it doesn't matter the equipment or skill level you bring, you're immediately embraced and taught a very solid curriculum. If you show up at one of the above mentioned competitions, you're at the mercy of the match director and staff, and the level of embrace and education is subject to how busy they happen to be that morning and how willing/able/interested they are in helping you (in addition to running their match and shooting it themselves). And let's not forget that the #1 piece of advice a new shooter gets at a shooting competition is a long shopping list of all the equipment and modifications they need in order to compete.
Granted there are a few "intro to IDPA" or "intro to high power" courses out there, but they're few and far between, and geared towards people who want to become serious competitors. There is a lot less out there for the casual, come-as-you-are shooter that Appleseed caters to.