Writing in the Polish language is perhaps the most difficult part of language, the disadvantage being that errors are visible for eternity, or at least until one tears up the paper. Obviously one can resort to the primary means of communication, speech. Writing was invented to give words permanence, what is written has sometimes lasted for centuries two even three thousand years and longer. Writing is much easier now, writing a letter or some other text on a computer is much less difficult than typewriting or handwriting and now we have spell-check.
Having listed all the substitutes for traditional writing one is forced to acknowledge that no e-mail or printed letter gives anything like as much pleasure as a handwritten birthday card or Christmas card. We all like receiving cards and letters, the problem is getting around to writing. However at least after thinking about it, it has been established that writing is important even if we do not rush to put pen to paper. Not everything that one writes becomes a historical document, far from it, shopping lists, simple instruction messages! Yet there are those occasions when absolutely nothing else will suffice. Great-aunt has died and unless you write to her daughter, she may well take mortal offence.
If you listen with understanding, speak and are understood, then given that you read there is no reason why you should not write. Just start with modest projects, writing the occasional letter and any other correspondence actually will complement your spoken Polish. How so? Because when writing one has the time to make sure that it is correct. In speech it is more important that the actor continues speaking even if making the odd mistake than he is correct but only speaks a word once in five minutes! Writing is the opportunity to do something without hurrying. To do a small thing but without error.
Actually I recommend writing on a computer and then copying the printed off text by hand onto the page of the letter or card, until practice enables you to dispense with the computer. Later on why should you restrict yourself to family social correspondence? Over the years hundreds and hundreds of authors have written books, which were published in their thousands. Many authors were criticised by their contemporaries but they continued writing and were still printed and sold. It is probable that everyone has one book inside them. Why not write it? Why not write it in Polish? It is not essential for written Polish to be written in professorial style. In fact it is probably better if it is not. When you speak you do not pretend to be somebody else; so when you write, write, as you would speak if you had the time to ensure that every word was spoken as you really wished to say it.
Far-fetched, exaggerated perhaps yet nonetheless true for all that, there is actually no reason why you should not write. The first time is always the first time, and the next time is always easier. Not only that for if you write then you may say that you listen to, speak, read and also write Polish.
Pisany jezyk takze jest formalniej niz mowiony jezyk. (I'll continue in English, only on account of Forum rules :) )
I find that the stylistic differences between speech and writing even more extreme in Polish than, say, in German or certainly, US English. Commercial French though, has about the strictest rules I know of among Western languages, for formal vs. informal usage.