ehh it's a distinction without a difference. The point is that alternative links are available to circumvent paid access for anyone that wants them.
The end result is exactly the same.
Substitute almost any disruptive public service to see the issue with your line of reasoning. For example - you seem to think that [ bulldozing private property ] to "construct an emergency fire break" is somehow different than [ bulldozing private property ] for any other reason.
Never mind that the sort of scraping being objected to is actually harmful to service health while what the wayback machine does is almost entirely unnoticeable.
A "scraper" is simply an automated process that fetches URLs intended for display to a human, and processes it. The act of scraping doesn't imply anything about:
1. The frequency of the fetches,
2. The way that the resulting page is processed.
Search engines scrape. Again, they have to. Same goes for archive.org.
Thing is, there aren't tens of thousands of search engines/archive.orgs that can overload a site at once.
Hence, distinction without a difference.
So Internet Archive, Archive.today, Archive.ph, etc. are all just means to the same end.
The internet archive is not designed to circumvent anything. It is not designed to "grant access without having your own access".
Archive.org exists to preserve historical snapshots of the public parts of websites, and not to bypass subscriptions or pay walls.
I think it's a distinction worth making.
Not to mention that the Wayback Machine itself isn't exactly a good tool to bypass paywalls as most paid sites don't let them archive paywalled content anyway.
archive.org is the more straight-laced archive that doesn't circumvent sites that try to block it, and removes content they deem 'problematic' even if not illegal or requested by the site owner.
Meanwhile archive.today/ph/is/etc is the guerrilla alternative run by a die-hard datahoarder that seeks to archive the information itself, bypassing whatever blockers/login pages/whathaveyou to achieve the result.
It's nice to have both options. When I archive a site, I usually use both for added resiliency.