I think academic scientists are criminally underpaid (especially at the NIH), and really hope something can be done to rectify this. However, I don’t think unionization is the way.
Ultimately, unions' power comes from the threat of striking. Unions' demands only have teeth because of their ability to completely suspend economic output for an entire company or industry. This is possible because economic output of most unionized industries is collective: a factory worker has no personal stake in the individual widgets that s/he makes, and thus can dispassionately suspend widget production along with everyone else in the union.
By contrast, science is extremely individualistic. Each "widget" is a scientific publication, which is directly attributed to a few specific contributors, and crucial for advancing an individual's scientific career. Thus, scientists are extremely passionate about their individual labor. Furthermore, science is often very time-sensitive — there is a huge premium on being the first to publish. Time sensitivity is especially high in the life sciences, since experiments with living things often cannot be easily scheduled around a strike.
Passionate, individually invested scientists are therefore much less likely to voluntarily suspend their work than dispassionate laborers in collective industries. This makes striking much less impactful (there will be a lot of scabs in a scientific union strike), thereby negating much of a scientific union's power.
(Imagine — you are an NIH postdoc working on a major publication in a hot field that will make or break your candidacy for a tenure-track faculty position. You are aware of several other labs working on the same project. Whoever publishes first gets most of the scientific accolades, and thus career advancement. The NIH union decides to strike. If you join the strike, it will set back your project, increasing the probability that one of the competing groups will scoop you, potentially greatly setting back your career. Are you going to let this happen?)