Is it inappropriate for a SSG to put a SGT in the front leaning rest?

Of course it is But NCO Business we correct behind closed doors, not in front of Joe.

It is perfectly acceptable if said SGT needs minor, non-judicial corrective action. The authority of the NCO is contained in AR 600-20, and also referred to in FM 7-22.7

Anecdotally, I had a squad member, Junior Enlisted, who was reminded to bring their ID to an appointment. As this was a standing order to do so, it was universally understood what the expectation was. When that Soldier did not have their ID Card, I have both the Soldier and the Team Leader, push-ups to do while I verbally counseled them for the failure to have the ID, and the failure of the Team Leader to conduct the required Precombat Checks.

We had an E-6 put an E-5 in FLR when I was in el paso.
The next morning the 1SG spoke to the entire company how disrespectful an act like that is and that if we are ever in a position like that in the future to take the junior nco aside and discuss things privately.

The front leaning rest is for privates. A leader must know how to correct others leaders without making it seem as if they are being punished. Yet a SSG, is still young and still learning how to become an effective leader.

I find positive correction too be the best way to deal with junior NCOs. Not only do you garner the respect of your peers, communication dialogue go a long way with mentoring those who are newly appointed to the non-commissioned officer corpse.

Based strictly off of how you wrote the question, I'd say no. I've been dropped by my SSG before. Was I in the wrong? Technically yes. Did I take it to heart? Nope. In the end I took it as he felt his NCOs dropped the ball and it took some corrective action to ensure it didn't happen again, and he wasn't the type to put things on paper if it didn't warrant it.

As long as it's not in front of Joes I'd say it's not inappropriate. Of course, context matters. But I end it with this, SGTs fuck up from time to time. And a little smoke sesh to remind a SGT that they fucked up is a hell of a lot better than putting shit on paper.

Yes. Anyone can be depending on attitude and professionalism. If they at a SGT and they act like a PV2 then coach and counseling them while smoking them. They act like a junior enlisted fresh off the block then they get treated like one. Reserve side I've seen 5's act disrespectful and know they are smoked but its in private. Like when my PSG dropped my PL, few knew about it but it still happened.
Otherwise I would hope the 5 receives guidance and opportunities for improvement but once done a few times, new tactic of dropping them. Remind them they still have to perform and listen.

SSG (Join to see) for me they have have to do something very F'ed up for me to put a SGT in the front leaning rest. I have always been told praise in public, punish in private. Still a firm believer in that. That's my two cents.

An order like this is not punishment. It is training. Get out to the "right to work" as a civilian, you can be fired for _____ (you fill in the blank). You have to learn to lead. You lead by teaching.

If you are doing a mass corrective measure for the platoon/squad/team. Sure.

If you are just singling our the SGT; yes and no.

Yes you can, but no you can’t do it when or where others can see.

Praise in public; reprimand in private.

PT push up demonstrator ;-)