This is one of the main sins of postmodernism: the thought that because all view points are tenable, all are correct. The scientific method is based on accuracy of prediction, otherwise we are not talking about science anymore. That's not bad, and many a researcher could do with the realization that maths and models are not the best way to describe all things. It's a different ballgame though.
I believe the point being made here is that, indeed, scientific method is based on accuracy of prediction. However, in order to reach a good accuracy, a great deal of fine-tuning and tweaking is required. E.g. high energy physics. The standard model has something like 18 free parameters. A new theory, which could be "more correct" and provide, in the long term, better predictions, might require time and manpower for…
You are talking as if this isn't the case already, for instance: https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Mo...
I don't think that the usefulness of alternative viewpoints is contested by anyone, the problematic part of the article is the vague, ill-informed critique of 'scientific rigor'.
What other way is there to judge models than to compare them with experimental results? Grounding theories to experiments is literally the only thing that separates science from crackpottery.
It's also pretty weird for the article to criticize "logical positivism", when the most common contemporary views on the topic of philosophy of science (e.g. Popper, Kuhn, Putnam) don't actually agree with logical positivism.