I don't understand why you think building alternative app stores is somehow a limiting factor. If you want to use some software, and the company wants to bypass Apple's protections, they'll just put a download link on their website. Why go through the hassle of registering with any "app store" at all?
Because Apple still wields control over iOS, which means they can also curate how the sideloading experience. I don't believe that even if legislation and regulator action forces iOS to permit sideloading, that it necessitates sideloading to be done in as casual a process as it is to download and install software on macOS, Windows, or desktops in general. Apple will still be able to determine how sideloading is done. And they can make the process very guarded, with multiple disclaimer screens and agreement menus that the user must assent to before they are allowed to sideload. Even on Android today, enabling sideloading is a multiple step process:
Furthermore, I believe that Apple can choose to shape the experience even after sideloading is enabled. They can add badge icons that single out sideloaded apps. They can force sideloaded apps to be on specifically marked pages on the springboard. They can add alerts and popovers galore that ask the user "Do you really want to do that?" wrt the sideloaded apps. Apple is a master of UX and branding - if they can influence millions of users via the blue iMessage bubble vs. the green SMS chat bubble dichotomy, they can find a way to subtly single out sideloaded apps as worthy of concern. Emergent user behavior then follows.
Finally, as I have mentioned in the previous link, Apple still controls the operating system that all apps, whether sideloaded or not, exist on. If they wanted to harden its security and strengthen entitlements in such a way that even sideloaded apps cannot bypass certain privacy or security safeguards, they can probably find a way. At they very least, they can introduce a similar notarization process that they already do on macOS on non-Mac App Store apps.
Everyone seems to keep forgetting, there is already an option on iOS for developers not wanting to go through the App Store: web apps. I believe WASM can even be used these days. Except that Safari doesn't offer developers some privacy sensitive APIs other browsers do. The current side loading pressure has very little to do avoiding Apple's cut and everything to do with bypassing Apple's restrictions.
So I expect should Apple introduce a heavily sandboxed side-loading experience, we'd be seeing developers complain they are not adhering to the spirit or the law or lawsuit.
PWAs have long failed to reach adoption on mobile- not just iOS, but also on Android- because of technical limitations that they have compared to native. And perhaps, lack of sufficient interest both from independent developers and from larger tech corporations. That interest is probably orthogonal to the sideloading battle.
Seeing as how Epic was the first company to launch a lawsuit against Apple's control of the App Store, and they certainly care more about avoiding Apple's cut, and little about privacy restrictions, that would seem to contradict your point. We haven't exactly seen Meta or Google throw in with Sweeney's crusade. Instead, the companies who have publicly supported the suit have all been companies that want to bypass the 30% cut, such as Spotify or Tinder.
Finally, if Apple introduces a heavily sandboxed sideloading experience (hopefully they will also introduce more privacy sensitive APIs to Safari as well!), then perhaps the courts will recognize that as a reasonable action and beneficial to consumers and the public interest, and will not press the matter further. There's only so much back and forth this sort of thing can wage on in the public, anyway. Lawsuits are costly in time, in attention, and in fees. If Apple does something in good faith, unlike what they've been doing in response to Dutch legislation (0), then presumably our systems of democracy will appreciate it.
