I think this is basically right. They've been unable or incapable of really implementing a coherent plan for the last few seasons due to the Wenger situation and the clashing time horizons it involved (him clearly having incentives to win now, despite that looking more and more unlikely over time).The bigger problem for Arsenal is that they have shown no strategic vision over the last few windows. So they sort of need a rebuild, but they also have several star players in their late primes, e.g. Ozil (29, assuming they keep him), Mkhtaryan (29) and Aubameyang (28). And they don't have any pieces in the 22-24 range who project to be big stars entering their primes in 2-3 seasons, besides maybe Bellerin (who may not stick around). The squad has been built to win now. It's possible a new manager, with one or two additions, could do a quick turnaround next season. Where that leaves Arsenal in two years though, as their big-money stars age, is a big question.
There's also the issue with top clubs that there's a big feedback loop. It's hard to sign great players if you're not in the Champions League, and hard to get back into the CL without great players. City and Chelsea can do it, but they can overpay in wages if they need to, can Arsenal do that? If Arsenal have a couple of seasons where they finish in midtable, will they still able to get Aubamayengs and Ozils to come play for them? They already lost Sanchez.
Its not an insurmountable problem going forward, but definitely one that needs to be handled well (which it might not be). As you note, in football it just doesn't pay to go into a complete rebuild. So the answer is really to build a team that relies upon a few veterans to remain competitive - Ozil, Auba, Mkhitaryan, Lacazette, Koscielny, Monreal - while making a concerted effort to buy and integrate a new core of younger players and improve upon some areas (CM, CB, and some more dynamic wing players) that have become weaknesses. The best thing they have in their favor in this regard is that all the veteran players just mentioned either signed new deals recently - knowing that Wenger would likely not be around for most of their contracts and probably also realizing that this team wasn't going to win the Champions League or anything in the next couple seasons - or, in the case of the defenders, are longtime club servants probably OK with sticking around. But you need to bring in the right new manager who will get along with those players and keep them on board. And you need to do a good job with recruitment and player development if you actually want to get better. Easier said than done for sure.
Its unclear if he would really leave Juve but I've heard some talk recently about Allegri wanting a new challenge (and a much richer contract) and I think he would be an excellent choice if truly available.