I think experts generally accept that "Waterfall" is a stereotype of certain ineffectual development practices.
From the 60s into the 90s, I dare say the vast majority of software developments - at least for business data processing - were not big-bang, one-shot projects conforming to "Waterfall", but incremental developments performed and readapted over many years by long-serving, permanent in-house staff. Let's call this "original agile", although I'm assigning the term retrospectively.
Amongst all the failures and uncertainties of this original-agile approach, and amongst an always-increasing software complexity, there was a growing tendency towards the stereotypical Waterfall practices.
The intention of Waterfall practices was to increase control and reduce risk, but in practice it failed to do those things. Instead its overheads just added to the cost, and its increased rigidities reduced the quality.
The intention of Waterfall was also for organisations to start treating software development like mechanised manufacturing, where the employer owns the machinery, the processes, the tools, and the know-how, and applies workers to perform the routine activities within an overall division of labour. This was as a fightback against the new kind of powerful craft workforce emerging in software development, just as the power of old craft workforces was being successfully destroyed by advancing mechanisation.
It's also worth noting that original-agile was completely inconsistent with the outsourcing and contracting business models that increased especially in the 90s, because with no limit on price nor with criteria for delivery, unscrupulous capitalist contractors would naturally just take the client for a ride and deliver nothing - or certainly charge twice as much as directly-employed labour would cost for the same delivery. So this was another reason to move towards Waterfall, because supposedly you could fix a price and hold a contractor legally liable for delivery to a spec.
The Agile Manifesto was a fightback against those currents. It reasserted a number of things, including the need for the skilled craft workforce over the use of drones following routine processes furnished by the organisation.
And it also invited contractor-clients to accept the reality of how development is done and always was done, and therefore accept the need to furnish money speculatively with no guarantee of quality or success. Control relies on reputations and a sense of professional purpose, and the power of the contractor-client to "sack" the contractor as the final disciplinary measure - which is much the kind of control employers have on directly-hired staff. I know this isn't how Agile contracting is generally sold, but is the reality of how it works in practice.
Meanwhile the so-called "Agile-Industrial Complex" nowadays is basically just another iteration of the forces behind Waterfall. Written documentation may be lighter, but the fundamental point of putting the workforce to work on routine tasks within a division of labour remains.
The equivalent of the old heavy documentation is now the heavy training and credentialism of "scrum masters" and non-technical "product owners" and various kinds of "daily ceremonies" and that sort of thing - the point is for the employer to own something, in this case an organisational structure and a set of routine practices (rather than the paperwork and routine practices of yesteryear's Waterfall), which supposedly allows it to hire drones and, if necessary, simply sack the incumbents and place new faces in all the same positions, and the work will carry on as before.
There is really only one way development is actually done, and ever has been done, and it is broadly consistent with "agile" on the supposed Agile-Waterfall axis. The essential meaning of what Agile is, is highly obfuscated by writings on the topic which come from the perspective of the Agile-Industrial Complex, but the crucial point is that basically development today, when done effectively, is being done on much the same terms as it was done in the 1960s.