How important is journal prestige when researchers publish a paper?
In principle, publishing in a prestigious journal may help reach many readers and/or boost your career. The practice of judging articles by the journals they appear in is widespread although also widely denounced (cf the San Francisco Declaration on Research Assessment).
In practice, a lot depends on your field of research, your career stage, and the organizations that pay your salary and/or grants. At one extreme, some people would boycott "luxury journals" as a matter of principle (Randy Schekman) or ignore journals altogether and just post their results on arXiv (Grigori Perelman). At the other extreme, some will tell you that their careers entirely depend on how many articles they publish in their discipline's elite journals.
I am completely disillusioned with prestige at this point in my academic career. It is all about the strength of the peer review committee for me now, nothing less.
I work on the intersection between engineering and computer science, so I get to read literature from both community and I cannot tell you how many completely **** paper makes it through the "peer review" process at top ML conferences/journals such as ICML, JMRL, ICLR, AAAI and NeurIPS. These "prestigious" journals are publishing crank-level papers with extraordinarily poor citation practices.
Of course, if you look at their peer review process then it is all revealed: two-three reviewers (possibly students) not too familiar with the field or the literature giving superficial and uncritical reviews to not hurt any feelings. There is an over-emphasis on simulation results, which are barely reproducible. Finally these reviews are rarely completely blind as well, because a paper is almost always simultaneously uploaded to Arxiv. Just because they are Google employees doesn't make their research good.
The same probably can be said for a minority of journals in engineering. I have definitely seen a share of bad papers here but I always ensure that they do not make it through.
It is all about the peer review process.
By comparing the CVs of academis who have permanent jobs with those who do not, you can show that publishing in a prestigious journal is, in fact, career changing. Having publications in prestigious journals is strongly correlated with later receiving a stable academic job.
This in no way means that everyone should spend all their time on trying to publish in those journals. For many people, worrying less about prestige would be life changing in a good way.