ignoring the other examples you've been given: it absolutely does even when it goes well. The scientific method is literally based on "other people must change and refine this, one person's work is not immutable nor should be taken as gospel"
Also what science is has changed. Science used to be natural philosophy and thus was combined with other non-scientific (to us) disciplines. Social sciences have only been around 200 years tops.
Some would debate that applied mathematics is science, others would say all sociology isn't science.
I'd argue the scientific method does not have to include multiple people at all. All it is, is the process of coming up with a hypothesis, designing an experiment to check that hypothesis, and then repeating while trying to control for external factors (like your own personal bias). You can absolutely do science on your own.
The broader field of academia and getting scientific papers published is more of a governance thing than science. You can come up with better hypotheses by reviewing other people's science, but that doesn't mean when a flat earther ignores all current consensus and does their own tests that it isn't still science.
I'd counter argue that a test that is not communicated, reported, described or otherwise transmitted to another party is identical to it not happening, therefore one needs to tell "someone" (even if that is a private journal), and while in theory falsifability is possible solo, it increases the problem of induction, and science is, in essence, a language: a description of phenomena not the phenomena itself.
I'd agree for the result to be useful to society, the science should be published. But science can still be useful to an individual without sharing. I use the scientific method regularly in my daily life for mundane things, and often it's just not worth the time to communicate to others because the situation is unique to me. I write it down for myself later, which doesn't make the science any less valid.
I'm explicitly arguing that you can separate the two. I can perform a completely independent experiment in my house.
For example:
I make a hypothesis that my stove can boil 1L of water in 10 minutes.
I then measure how long my stove takes to boil that water.
I can then record these results to inform my future cooking and water boiling experiments.
Proper use of the scientific method may also attempt to measure atmospheric pressure, water contaminants, and other factors that may affect the result.
I don't have to publish the results anywhere or even talk with another person, yet I've still used the scientific method. I'm not a professional scientist, but I am an amateur one.
I can perform a completely independent experiments in my house.
And I can scream into the abyss, it's just as relevant. The absolute majority of actually useful and relevant science is performed socially for social purposes.
I make a hypothesis that my stove can boil 1L of water in 10 minutes.
You aren't even supposed to do a scientific experiment in the way you have just described. Or rather, there is neither a universally agreed upon scientific method, nor would your described experiment hold up to any standards.
An actual scientific experiment into water boiling would involve at the minimum
A model predicting the speed of boiling based on relevant variables
A collection of many data, and preferably corroborated by independent sources
Statistical analysis of the data (there are many methods to choose from) to gauge confidence in the model.
Publishing or proofreading of the results.
However, at each of these steps, you have a choice of how to approach the problem. And this depends on what you are trying to do, and what the best standards in the industry are. The process has also changed over time.
And this reveals the problem of many people's metaphysical approach to science. They treat it as if it were a platonic ideal, or floating constant in the human minds pace. In reality, "science" is an industry with its ever-changing standards, culture, interaction with the rest of society, and a million other complexities.
I think we have a fundamental disagreement on what counts as science, and that's okay.
Your methodology seems to imply a valid scientific experiment must be sufficiently rigorous as to improve on the current scientific consensus. And I do partially agree, it's a waste of time collecting data that's just going to be worse than previously collected, more controlled experiments.
By my philosophy is a lot looser. To quote Adam Savage:
"The only difference between screwing around and science, is writing it down"
The truth doesn’t change. Scientific consensus does. Scientific consensus has been wrong on countless things. After all, science is about getting things a little less wrong every time.