To some extent, if, as a journal, you have to start policing submissions in the ways described, you have already lost. In that so much of the journal industry is not about sharing knowledge, but about generating a metric (publication count) for profit. Rather than create more hoops that are only going to push good science away to other venues, they should reconsider what they are trying to accomplish overall, and where appropriate, go out of business.
I feel like this is less a problem of serious science (where it's generally known what authors and journals are reliable, and where people using the results of others know enough to subject them to scruitiny). It is a problem of the publishing industry and of evaluating academics for tenure and promotion.
I think even serious science can be problematic, at least to the extent that "generally known" means wildly different things across different subfields. During graduate rotations I encountered a few instances where something was known to be very hard to replicate, but it was basically impossible to find that information publicly. So if you didn't happen to "network" with labs that were aware of this (which could occur for a variety of reasons besides just being early career), you could end up wasting a lot of time trying to build on work that is at best very finicky, if not outright wrong.
Trusting only the work of specific authors may not be a bad strategy, albeit quite conservative. But trusting work because of the journal or the university it came from is way more likely to yield misses IMO. Not saying there isn't a correlation, just that there's still plenty of bad science going on at supposedly top institutions. And I've lost count of how many times a supposedly big result published in Nature or Science just quietly drops off the face of the earth. No rebuttal or retraction, but 10 years go by and nobody in another lab does any real followup on a seemingly cool result? I find that quite sketchy.
Biology papers are especially bad at not releasing raw data or detailed methodology, so in some cases it's not possible for even a very educated person to evaluate the quality of the work from reading the paper. There's definitely some trust that goes into it, probably too much given how oversubscribed/hypercompetitive that field is.
I feel like this is less a problem of serious science (where it's generally known what authors and journals are reliable, and where people using the results of others know enough to subject them to scruitiny). It is a problem of the publishing industry and of evaluating academics for tenure and promotion.