Most of the researchers focus on publishing with indexing journals as the main academic aim. With ignoring some ethical aspects like there are several non-journals has a good editorial board or it present experienced reviewers.
I think that the hunt for high-ranking journals and citation measures is doing harm to science. Journals have also other qualities besides their impact factors. See also this discussion: https://www.researchgate.net/post/Publishing_only_in_the_journals_with_high_impact_factors_or_publishing_good_papers_no_matter_IF_or_no_IF_journal_and_achieving_high_citation_score2 . However, I understand that there is a pressure for this hunt from scientific organisations and decision makers looking only on seemingly "objective" measures. See this discussion on a petition (https://www.researchgate.net/post/Petition_Stop_Tracking_Science) demanding also that "All actors in science governance must redesign their decision-making and evaluation instruments and overcome their fixation on bibliometric indicators."
Yes there are certainly quite a few non-indexed journals with great editorial board and review team. The reason behind indexing is mainly due to quality control of the research article, optimum circulation and to discard the predatory journals. Hence, most of the PhD committee are suggesting researchers to publish their articles in a peer-reviewed indexed journals for better assessment.
First, the term - 'Indexing journals' makes no sense alone, in my view. Any journal can be indexed (or abstracted) anywhere, either in a crawler-based database or in a manual/human indexing database. Thus, it is more appropriate to indicate the location of indexing/abstracting too. The recent research in 'publishing' shows that authors' significant concern in publishing their articles in journals which are included in reputed databases (mainly manually indexed databases like Scopus, WoS, Medline, etc.). The inclusion of journals in 'selective' databases ascertain the 'status' of a journal to some extent. For example, excluding deceptive journals can be expected from these databases. However, there could be exceptions. I've seen some journals that are blacklisted include in Scopus, not very often though. In addition, improving the visibility of publications is another important benefit you can gain in publishing in journals included in these databases. Research institutions concern the publications included in reputed A&I databases for promotion and tenure since these journals are 'selective'. However, there could be good/genuine journals that are not included in these reputed databases and there could be numerous reasons behind this.