Yes, proof of the scientific method in experiments should be required for publication in all peer-reviewed journals, because this is a good way to ensure that the work that is done is reliable. With so many scientific experiments being done with an end in mind, often political, the scientific method is a helpful way to determine whether the work is valid.
Scientist are constantly improving on each others ideas and learning from the scientific community. One of the ways they learn from that community are experiments from other scientists published in peer-reviewed journals. In order to ensure that the information they are receiving from those journals is accurate, the publishing scientist should show how he used the scientific method to arrive at the results of his experiment.
The scientific method is what science is built on fundamentally. Sure, it was born of philosophy, but the scientific method is where the magic takes place. You should demonstrate that you used the scientific method if you are going to publish something for peer review. It makes the process more smooth and easier to believe.
I believe proof of the scientific method in experiments should be required for publication in all peer-reviewed journals. I believe there have been to many instances where a group tries to recreate a trial and gets completely different results, which leads a person to believe that things were not done properly the first time around. I believe these instances need to be diminished and this requirement may help.
The scientific method is not always laid out in full detail, but the concerns of the reader over whether the scientific method are used will become obvious to someone who reads it. Peer-Reviewed journals have been analyzed by scientists in the field of study and have either agreed that it is possible, or will label the information as fraudulent or possibly just incomplete.