I have seen a lot of negative reviews and even boycotts of some Elsevier journals. I do not want to jeopardize the future of my academic career by publishing in illegitimate journals. Am I correct in assuming that the journals on Elsevier are considered "legit" but just "very pricey," and this is the source of the negative reviews? Would it be safe to publish on any journal of Elsevier?
They're generally legitimate. The negative reviews and boycotts aren't about the quality of the journal, but are because of Elsevier's alleged high prices (see The Cost of Knowledge). Elsevier publishes some of the best journals in some fields, e.g. The Lancet and Cell.
Having said that Elsevier gives their editorial boards some leeway on what to do with their journals, and to my knowledge up until recently that included not conducting peer review if they don't think it's necessary or appropriate. This journal Medical Hypotheses was an example. That journal published a paper denying that AIDS is caused by HIV, there was a backlash, and Elsevier replaced the editor-in-chief. Although you should be fine in general if you publish with Elsevier, to be sure, you'll have to research the journal in question.
Clarivate has a list of journals that have been punished for excessive self-citation. Several are published by Elsevier. However, all the biggest publishers have journals that have been punished.
No publisher is completely reliable.
A single case of corruption can even span multiple publishers.
There may be some reputable Elsevier journals, but some of them are certainly not legitimate. As an example, Toxicology Reports publishes work by the the editor-in-chief in a special issue organized by the editor-in-chief overseen editorially by the editor-in-chief (passed off to his buddy when the issue was raised) in which they take the data in the VAERS database as actually representing effects due to the vaccine as opposed to correlated in time with the injection and have the audacity to suggest that the actual real incidence of reactions attributed to the vaccines are a factor of 10 higher, then say they are making "conservative" estimates.
Actually, Elsevier is not at all a credible and reliable publishing house. If you are known to the Editors or you are paying them, you will be able to publish, or else keep things about that your work is not worth publishing. It is not even beneficial to publish your paper in this publishing house. The students are influenced by their IF. But I would like to tell you truth that they have a self-citation of more than 60% in all their journals, which ultimately, provides you with a fake IF. Think wisely and choose wisely.