Wherein the point I was setting up in Compression is made.
What was the point of that little discussion about compression? Talking about compression is a pure way to introduce a general principle: To make one thing easier, something else must be made harder.
Consider a C compiler, and the C language it defines. It makes "subroutines" much easier to deal with, but at the cost of not allowing you arbitrary sequences of machine code. You can embed assembler, but even then the assembler code can't be arbitrary. It must work in harmony with the rest of the C code.
Examples can be seen everywhere you look, once you know what you're looking for. Take two top languages from two different paradigms and pit the strengths of one against the weaknesses of the other. Watch a simple Prolog exercise devolve into a multi-thousand-line C program, because Prolog makes easy some things C makes hard. On the other hand, imagine trying to write the Linux kernel in Prolog; C makes many things easy that Prolog makes hard, or even impossible. The compilers that implement these languages had to make different tradeoffs; a correct choice for C may be horribly wrong in some other context.
Many people believe that the purpose of higher-level languages is to add power, but the best way to think about it is that they are taking away power, so they can trade that power in for some other benefit. No language, however clever, can actually add power to machine code; machine code is the very definition of the capability of the machine itself. A language can only manifest as limitations on the machine language the machine may actually execute. But in return, all the features that we normally think of as ``added'' features are actually built on these chosen limitations.
When learning a new language, the first thing to do is to seek out what the language forbids, and why it forbids them. The second is to find out what the language builds on top of those restrictions. For reasons that should be obvious, few languages loudly advertise the things they forbid, so this may take some research but you can usually find it. Beginner exercises: Find out what Java forbids, and why; find out why functional languages are so keen on immutability, and what restriction that names.
Nothing is free. If you want to make some compiled output or result easier to generate, you must make others harder or even impossible. If somebody is telling you something is free, that's just a sign to look even harder for the tradeoff; it must be a doozy if they're trying to hide it that hard. (Or maybe they're just ignorant. But one thing they aren't is right.)