But isn't the very point of \include command to work separately from a long document?
True, but it’s not the point of the \include command to include complete documents, as you’re trying to do; rather, it works on fragments of a document.
What's the point if I can't compile the including file separately (having no preamble, etc)?
The point isn’t that you have complete documents. If you want to compile just some chapters but not others, you can use the \includeonly command to specify which chapters to include, and which not to include.
Is \include the best option for working on, say, a chapter of a long document separately?
It’s the best option that’s ready-made. You can however create your own macro that may work better for your specific circumstance (that’s what I have done for my master thesis).
For your specific use-case you could create a new macro that disables the \documentclass, \usepackage and \begin/end{document} commands. For instance, this might look as follows (untested!):
\newcommand\includedocument[1]{%
\begingroup
\renewcommand\documentclass[2][]{}
\renewcommand\usepackage[2][]{}
\let\document\relax
\let\enddocument\relax
\include{#1}
\endgroup}