What I was personally referring to when I mentioned "software" is a photo editing application like Photoshop, Lightroom, DxO Photolab, etc. The subscriptions/purchase prices of these type of software is $200+. There are free software versions of these apps but most photographers do not use them.
Sorry, to be extra clear, my point is that you will not get these results without such software, because photos almost universally require editing in order to look their best. But my belief is that Apple, with their "Shot on iPhone" marketing, is trying to convey that you will get these results straight out of the camera. This is unlikely to actually be the case. That's the sum of my point w.r.t. software.
You can get 98% of the same capability with much cheaper software - you don't need spend several hundred on software (affinity photos does focus stacking raws, for example). But you're right the best looking photos are usually processed somehow.
I use lightroom for many years, but when it went subscription only and I couldn't install it from disc anymore, I bought affinity photo. I think I've saved hundreds of dollars already.