What REALLY happens when you don't free after malloc?
Just about every modern operating system will recover all the allocated memory space after a program exits. The only exception I can think of might be something like Palm OS where the program's static storage and runtime memory are pretty much the same thing, so not freeing might cause the program to take up more storage. (I'm only speculating here.)
So generally, there's no harm in it, except the runtime cost of having more storage than you need. Certainly in the example you give, you want to keep the memory for a variable that might be used until it's cleared.
However, it's considered good style to free memory as soon as you don't need it any more, and to free anything you still have around on program exit. It's more of an exercise in knowing what memory you're using, and thinking about whether you still need it. If you don't keep track, you might have memory leaks.
On the other hand, the similar admonition to close your files on exit has a much more concrete result - if you don't, the data you wrote to them might not get flushed, or if they're a temp file, they might not get deleted when you're done. Also, database handles should have their transactions committed and then closed when you're done with them. Similarly, if you're using an object oriented language like C++ or Objective C, not freeing an object when you're done with it will mean the destructor will never get called, and any resources the class is responsible might not get cleaned up.
Yes you are right, your example doesn't do any harm (at least not on most modern operating systems). All the memory allocated by your process will be recovered by the operating system once the process exits.
Source: Allocation and GC Myths (PostScript alert!)
Allocation Myth 4: Non-garbage-collected programs should always deallocate all memory they allocate.
The Truth: Omitted deallocations in frequently executed code cause growing leaks. They are rarely acceptable. but Programs that retain most allocated memory until program exit often perform better without any intervening deallocation. Malloc is much easier to implement if there is no free.
In most cases, deallocating memory just before program exit is pointless. The OS will reclaim it anyway. Free will touch and page in the dead objects; the OS won't.
Consequence: Be careful with "leak detectors" that count allocations. Some "leaks" are good!
That said, you should really try to avoid all memory leaks!
Second question: your design is ok. If you need to store something until your application exits then its ok to do this with dynamic memory allocation. If you don't know the required size upfront, you can't use statically allocated memory.
=== What about future proofing and code reuse? ===
If you don't write the code to free the objects, then you are limiting the code to only being safe to use when you can depend on the memory being free'd by the process being closed ... i.e. small one-time use projects or "throw-away"[1] projects)... where you know when the process will end.
If you do write the code that free()s all your dynamically allocated memory, then you are future proofing the code and letting others use it in a larger project.
[1] regarding "throw-away" projects. Code used in "Throw-away" projects has a way of not being thrown away. Next thing you know ten years have passed and your "throw-away" code is still being used).
I heard a story about some guy who wrote some code just for fun to make his hardware work better. He said "just a hobby, won't be big and professional". Years later lots of people are using his "hobby" code.