This is how I look at it...
If you think of painting/art you can draw some useful parallels
Trying to write without thinking of a genre is like painting an "abstract" painting - to some it will be a complete mess and to others (and probably the artist themselves) it will be a masterpiece
If the abstract painting "kind of looks like" an apple many people will think it is just a bad painting of an apple - and others will like it for "breaking boundaries"
If, however, you decide to draw/paint an apple then people looking at it will be able to make a direct judgement as to how "good" the painting is - i.e. How much does it look like an apple - but there is sooo much more - how good is the lighting, what medium was used (oil, charcoal, watercolour etc.), what is the composition like, is there anything else in the picture (a person, an animal, a landscape background)
I think this is why songwriters (especially those new to writing) get a bit nervous aiming for a particular genre - it will inevitably lead to direct comparisons and it is easy for a shot at "chart pop" to end up as "cheesey pop" - in the same way someone wanting to draw a perfect apple may get the perspective wrong
As in the example above, just because you have chosen a particular genre (i.e. to draw an apple) it doesn't mean that it is limiting in any way as there is plenty you can do to keep it interesting
However, if your art forms is a good representation of what you are aiming for - i.e. It is clearly within a genre (or the painting looks like an apple) it is more likely to be appreciated by the "man in the street"