The idea of Batman is that he'll be more effective if he makes himself into a legend, something larger than human. The reason he dresses like a bat is to wrap himself up in a mythology, to prey on superstition, it's marketing, it's psychological warfare.
The burning bat was a challenge to Banes authority, announcing to the city that Batman was back, and still capable of doing the impossible. It gives those who might want to resist Bane a banner to rally around and strengthens their courage. It puts fear in the hearts of Banes thugs, everyone who got out of Blackgate would have felt a chill go up their spine when they seen that.
This is exactly what Batman is, if you think it's silly or unrealistic that's fair enough, however I think you need to accept that basic concept if your going to engage with Batman stories.
