I'm less cynical than others. Join if you think you want to have a voice in the profession. Students have a surprisingly outsized voice in the AOA. We have more voting power in the AOA as a random student (in the right positions) than most random docs. The students at PCOM were the ones who wrote the amendment on the AOA side to merge.
Personally, I don't think joining clubs for CV items matters unless you were board. Even then, it's a very small item. So if you don't enjoy it, don't sweat it. Your sanity and extra time for boards is probably more important. Also, i don't think any of the perks justify the expense.
So only join if you like politics. Which I feel like most people actually do. Everyone seems to have an opinion on everything. Especially on the things related to the AOA. There's no better, or even other, way to change the AOA than to show up.
Show up, be respectful, and lots of people will listen. I showed up to the SOMA events as a relative conservative and everyone was respectful. SOMA showed up to the AOA as hyper liberals, and honestly, all attendings were respectful. What's more, they mostly took us pretty seriously even if they ended up disagreeing with most of us.
FWIW, the AMA side is AMSA or the county medical association/society/organization club. DO students are invited to these events. And like with SOMA and the AOA, AMSA has a voice within the AMA. You're given more power than you think as students. To give more specifics, the AOA and the AMA allocate votes to students. The AOA gives students WAYY more votes than the AMA, but both allow us to be represented.
If you join SOMA to go to national events, join as the national liaison officer or president. Those two are the two who the school will likely bankroll to go to events.