Research is of types. Not all types of research call for statistical analysis. Research that is empirical in nature must involve statistics at the point of data collection and analysis. And most researches are empirical. However, unempirical research, which does not call for statistical analysis, exists.

There are non-statistical publications. Observational studies with a detailed case history of one patient is an example. However, science requires statistics. Statistics is a way to account for the variability in results. Otherwise, why not take 10 observations and select the one observation per treatment that shows your ideal of what should happen? Statistics is a way to plan your experiment. How do you choose your samples and why? How many replicates of each treatment should you have? How many variables will you measure, and how will you extract patterns from this data? Even if all the world's complexity could be broken down into two means and a t-test ... we would still use statistics.

The way that you try to understand the system that you study will be constrained by your ability to design experiments. In some cases, the outcome that you get from an experiment is determined by how you have asked the question, and how you ask the question is limited by statistical skill.

Everything in graduate school was done with statistics which was generally accepted as a necessary part of showing quality work.

Decades later one of the non traditional colleges in California lost its legal authority to operate in part because it accepted graduate dissertations with no statistical content.

Research without a statistic is always suspect of inferior work. I suppose you could mount a campaign to change the expectation, It is likely to fail, but not for sure. which demonstrates the need for statistics to evaluate your chances.