Some postdoc positions are formally advertised. Arguably, even more exist on a "gray market" - they are not advertised, and a person seeking a postdoc is supposed to contact a professor directly. 

One ethical concern that I see here is that in some situations even when the agreement between the professor and prospective candidate is made, the position still has to be advertised (e.g. this may be a legal obligation in some countries). The advertisement will attract a number of applications, none of which has a chance to succeed, since the deal about this position has already been made behind the curtains.

My second concern is a bit harder to formalise. Is it true that when a candidate approaches a professor with a request like this, some serious ethical restrictions arise? Is it more difficult to turn the offer down, if you were the one asking for it? Is it more difficult to terminate the postdoc contract earlier than expected (and move to permanent position, for example), if you were the one asking for it? 

Should I keep trying to apply only for a officially advertised positions, or should I give up and approach senior professors directly?