With LaTeX, I know you can put pictures in the documents, use different fonts, ... and practically do whatever you want (except the fact that your document must have a predefined style, imposed by the macro packages you are using); instead, in TeX, you are absolutely free to dispose thing in the page as you like. But, in TeX, it seems (at least according to me) that you can't do things you can do with LaTeX, e.g., putting pictures in the pages. Is this the truth or is that I'm ignorant in it?
You are asking the wrong question. The real question is whether you can do in LaTeX all you can do in TeX? LaTeX is a set of TeX macros created by Leslie Lamport with the idea that a typical TeX user is not an expert in Typography and even if she/he was, her/his primary concern should be the document content—not the format. On another hand, TeX is a complete typesetting engine/language which is created to enable inexpensive production of relatively high quality documents in Typographical sense. Both TeX and LaTeX have completely succeeded in completing original goals. While arguably you can produce documents of better typographical quality with hot metal typesetting (deep typesetting) and Phototypesetting, with TeX you can do almost as good for the tiny fraction of the price. While TeX is typographic system, it has not removed the need for a typographer—a professional who is suppose to edit the document layout according to rules of typography. LaTeX has also accomplished its original goal and removed the need for a professional typographer for the creation of large classes of documents at least in practice. No Mathematics department and few if any publishers now have typographers on their payroll. I concede that typographic quality of typical LaTeX document is debatable.
Now going to your original question—if your goal is to create a generic mathematics article it would be quite foolish that you use TeX as it would require that you essentially re-implement certain parts of LaTeX. It is not impossible though. If your goal is to create a truly unique document you would be foolish to use LaTeX as you would have to fight pre-built document classes and you could still fail. Even something as simple as creating a documents with the letter of arbitrary size is non-trivial in LaTeX and involves use of third party packages.
I would also like to bring to your attention ConTeXt which was created to easy the use of TeX in a radically different way than LaTeX. ConTeXt is not trying to tell you how your document should look like. It expected that you are an expert in typography. It just makes it easy to create stunning documents in the fraction of time it would take it with TeX by a heavy use of key value parameters. Note that unlike LaTeX which requires tons of third party packages for a document of relatively modest complexity, ConTeXt is self contained. Everything you need is already in the "core" ConTeXt.
Yes, whatever can be done in LaTeX can be of course done in Plain TeX. If your aim is to write a simple paper using Computer Modern and seven bit fonts, or a novel in English without fancy graphics, Plain TeX is maybe the best tool. If you'd like to add support for UTF-8 encoding, you can use Plain XeTeX or LuaTeX, so you can also change fonts rather easily. That's all. Graphics are not really a problem, because PGF and TikZ run also over Plain.
Would you try starting a critical edition work with Plain TeX? Would you implement code listings with syntax coloring? Multiple indices, automatic cross references and numbering, multiple tables of contents? These must be implemented anew. What about commented bibliographies split by chapter? No,
biblatex doesn't run over Plain and there's no interface to Biber available.
You're starting from a false premise and, as you probably know, ex falso quodlibet sequitur
except the fact that your document must have a predefined style, imposed by the macro packages you are using
This statement is untrue: with a document class such as
memoir you can rather easily change every small detail of the output format and have at your disposal the hundreds of LaTeX packages. There are scores of other LaTeX class files that can even be customized at will.
Suppose you want to write a program for number crunching. Well, you have C, don't you? If you follow your idea, you wouldn't link to Octave, PARI-GP or other programs that would force you to use their API.
LaTeX is like a big set of libraries built over the basic TeX language. Using it poses no limits to your freedom. But it avoids having to reinvent hot water.