Mathematics is the kingdom of all sciences, every scientific phenomena can be measured, scaled, weighted and numbered within the principals of Mathematics. All other sciences are playing the role of databases for Mathematics and they are visible in every instant f life.

I would say no not necessarily, "the sum of the parts is greater than the whole" perhaps sit down and look at the entire syllabus and see that each of the categories of STEM get equal attention in terms of the learning outcomes for the entire syllabus. But if you try to include all into every activity it becomes very unwielding and difficult to implement in practice.

The biggest problem with this thinking is that all of those terms are far too broad to design detailed and specific learning outcomes. You might argue that all of those disciplines will influence how we shape the requirements of the teaching method, but ultimately applied are often driven 'bottom up'. Such that we start at the problem and design a teaching framework around the measures we can place on how well the problem is solved.

For example: If I am attempting to teach somebody a practical skill such as welding, my metrics are going to be a lot more specific and goal-driven (I.E. has it penetrated correctly, is the surface reasonably 'clean') than trying to start at the abstract end of STEM and work out what mathematics / technology I want to teach in the process. Eventually, under a QA / teaching review I might decide that the welder should undertake some kind of arithmetic assessment to hit the "M" part, or perhaps understand some of the metallurgical process for the "T" component etc... but that is more than likely secondary to ensuring that they are welding correctly and at a sufficient rate / quality point.

For modern education activities that are perhaps a bit more abstract (such as classroom staples of mathematics and essential sciences) then you could certainly use all four components to enrich the lesson. For example: take a lesson on organic chemistry (such as Alkene reactions) which covers "S" - we could add information about catalysts for "T", applications of chemicals or reaction rates / equilibria for "E" and some basic equation balancing or empirical calculus (such as exponential cooling or thermal model) for "M". However, you only have a certain amount of time to teach somebody and they can only retain a certain volume of information, so we are back with the earlier philosophy that the teaching method is usually more specific and drive by what the outcome needs are, rather than using STEM vernacular to guide teaching.

Personally, I think you should strive to attain something from all 4, but that is only a very basic high level assessment of general education. There are so many skill areas that you'll be unaware of until you spend time working with / or become an expert(s) in the given problem space.