I'm not being argumentative. You made a category error, I pointed it out.
It is my personal view of an aspect of science biased by my xperience. Nothing more than that. It was not uncommon for disputes to arise due to interpretations of words, resolved by numbers and math. And at that sometimes a dispute continued despite hard data and theory and demonstration
When you write mass, meter, energy, heat, second on paper it is SI. If you want to argue the SI with the base units of time, mass, and length along with the unit for work, energy, and heat are not foundational, take the last word.
That's a very long-winded way to say "I was wrong, and I apologize".
Indeed, it looks, to an unskilled observer, as though you are repeating your error.
SI is one of an infinitude of possible ways to formalize a system of measurements. It's special to humans, because it's the one we chose to use as a universal standard (despite which it is taking a very long time to bring the last few hold-outs into the fold); There will likely always be niche areas of science, particularly when dealing with the very large or very small, where other systems are more comfortable to use, and where SI will not be adopted for a very long time - if ever.
There is nothing fundamental or special about SI. It's a convenient set of standards for our circumstances. To say that SI is the foundation of science is to put the cart well and truly in front of the horse. The needs of science and engineering led to the eventual agreement to adopt SI. Not the other way around.
It has become sufficiently widespread that all students need to learn it very early on in their scientific education (although, outside the USA and Liberia, they will already know it well by the time they reach their first science classes), but that's not because it's special, important, or irreplaceable - it's just because it's been universally adopted. We all agree to use SI, just as we all agree to use base 10* for counting, because, of the infinite number of options, it is one of the more sensible approaches for humans to take.
* By the way, all number systems are base 10.