If you realize that what we remember are the extremized strawman versions of the complaints then you can realize that they were not wrong.

Writing did eliminate the need for memorization. How many people could quote a poem today? When oral history was predominant, it was necessary in each tribe for someone to learn the stories. We have much less of that today. Writing preserves accuracy much more (up to conquerors burning down libraries, whereas it would have taken genocide before), but to hear a person stand up and quote Desiderata from memory is a touching experience to the human condition.

Scribes took over that act of memorization. Copying something lends itself to memorization. If you have ever volunteered extensively for project Gutenberg you can also witness a similar experience: reading for typos solidifies the story into your mind in a way that casual writing doesn't. In losing scribes we lost prioritization of texts and this class of person with intimate knowledge of important historical works. With the addition of copyright we have even lost some texts. We gained the higher availability of works and lower marginal costs. The lower marginal costs led to...

Pulp fiction. I think very few people (but I would be disappointed if it was no one) would argue that Dan Brown's da Vinci Code is on the same level as War and Peace. From here magazines were created, even cheaper paper, rags some would call them (or use that to refer to tabloids). Of course this also enabled newspapers to flourish. People started to read things for entertainment, text lost its solemnity. The importance of written word diminished on average as the words being printed became more banal.

TV and the internet led to the destruction of printed news, and so on. This is already a wall of text so I won't continue, but you can see how it goes:

Technology is a double edged sword, we may gain something but we also can and did lose some things. Whether it was progress or not is generally a normative question that often a majority agrees with in one sense or another but there are generational differences in those norms.

In the same way that overuse of a calculator leads to atrophy of arithmetic skills, overuse of a car leads to atrophy of walking muscles, why wouldn't overuse of a tool to write essays for you lead to atrophy of your ability to write an essay? The real reason to doubt the study is because its conclusion seems so obvious that it may be too easy for some to believe and hide poor statistical power or p-hacking.