All the districts have formed a coalition and they have cut off power supply and food supply to the Capitol. That mountain hangar in district 2 has been disabled as well, so the Capitol cannot mount an effective attack. So why do they need to attack the Capitol? They can just camp outside and let the Capitol starve. They can shoot down any aircraft that leaves. It's an easy victory without unnecessary bloodshed. Sure, Snow might escape but is his life really worth so much trouble? Even if he does escape, he has no power to do anything.
Because they want a glorious victory.
Sitting outside quietly and letting the Capitol starve might win them the war in the end, but it wouldn't be a very spectacular way to end it all. Remember that one of the chief advisors to Coin is a master of public relations and used to be a Head Gamemaker. From a PR point of view, an active and highly visible victory in the heart of the Capitol itself would be a much more fitting end to the war than a passive victory and Snow's surrender due to lack of supplies. It showcases the military might of the rebellion, and ensures that nobody else will be likely to rebel against the new establishment in the near future.
This argument works from a practical as well as a PR point of view. Revolutions are based on fire and impulse. Sure, District 13 has a well-planned strategy, a huge military arsenal, and a rigorously organised force. But the other Districts have risen up more or less impulsively in their hatred against Snow, the Capitol, and the Games. If the war turned into an extended siege, it wouldn't take long for their fire to die down and many of them to get bored and go back home. The rebel forces will grow weaker, if anything, as time goes on.
Because they don't know what resources the Capitol might have.
The Capitol's ability to set up the minefield of traps and pods shows that they still have a good deal of military resources at their disposal. If the rebels simply sit and wait, the Capitol might be able to roll out some new weapon or strategy and inflict larger losses on the rebels than they would sustain by simply marching into the city. It's safer to hit them while they're weak and disoriented than to wait, possibly allowing them to gather their wits and have a better chance in the final battle.
And as well as military resources, there's also supplies to be considered. The Capitol might have a massive storage bunker somewhere in the city with enough food for years. Who knows, with all their technology they might even have a way of creating food. There's no guarantee that starving them out would even work, when they don't know how much food the Capitol might have.
Because their real target is the Capitol leaders, not the populace.
A siege would harm the poorest citizens of the Capitol more than anyone else. The slaves and Avoxes would be the first to die, and you can bet your life that President Snow would have the last morsel of food for himself. Now President Coin personally probably doesn't give much more of a damn about the common people than Snow does, but when you're the leader of a popular rebellion, you have to at least give the appearance of caring about the lower orders.
Conversely, all-out attack is a strategy which promotes speed. A swift rebel victory, ending the war in a matter of days, ensured that they had the Capitol leaders captured and incarcerated (or more likely executed) before they had a chance to create much of a 'human shield'. Note that this was exactly Snow's final tactic: using Capitol children as a shield for himself. Given more time, he would have been able to do this more effectively. Striking quickly to the heart of the Capitol, while it did mean a lot of collateral damage to buildings and property, probably saved the lives of a lot of the less privileged Capitol citizens whose starved bodies might otherwise have been used to protect Snow and the other top dogs.
This is just speculation, but maybe they need to take the Capitol by force. They are trying to prove that they are a threat, and what better way to do that than to strike quickly and powerfully at the center of the enemies. If they hope to have the people accept them as a serious government, they might think that laying siege would look like a coward's game, that the people will accept them more than if they just strike.