There are a few different realities here. First, it's not really whether you can get tenure with the publications, because almost none of the major respected journals accept simple null/negative results for publication. It's too "boring". Now, they do occasionally publish "surprising" null/negative results, but that's usually do to rivalry or scandal.

The counter example to some extent is medical/drug control trials, but those are pharma driven, and gov published though an academic could be on the paper, and it might find its way onto a tenure review.

Second, in the beginning there is funding. If you don't have a grant for it, you don't do the research. Most grants are for "discoveries" and those only come about from "positive" scientific results. So the first path to this is to pay people to run the experiments (that nobody wants to see "fail"). Then, you have to trust that the people running them don't screw up the actual experiment, because there are an almost infinite number of ways to do things wrong, and only experts can even make things work at all for difficult modern science. Then you hope that the statistics are done well and not skewed, and hope a major journal publishes.

Third, could a Journal of Negative Results that only published well run experiments, by respected experts, with good statistics and minimal bias be profitable? I don't know, a few exist, but I think it would take government or charity to get it off the ground, and a few big names to get people reading it for prestige. Otherwise, we're just talking about something on par with arXiv.org. It can't just be a journal that publishes every negative result or somehow reviewers have to experts in everything, since properly reviewing negative results from many fields is a HUGE challenge.

My experience writing, and getting grants/research funded, is that there's a lot of bootstrapping where you use some initial funding to do research on some interesting topics and get some initial results, before you then propose to "do" that research (which you have high confidence will succeed) so that you can get funding to finish the next phase of research (and confirm the original work) to get the next grant. It's a cycle, and you don't dare break it, because if you "fail" to get "good" results from your research, and you don't get published, then your proposals for the next set of grants will be viewed very negatively!