What is the use of Swift Silence?
Assuming you play your Bolts right your opponent can counter at most 1 of them.
This is what happens:

You have priority, you cast Bolt, Guttersnipe triggers, you have priority again
You pass priority, your opponent gains priority and can cast their counter if they want to, eventually they also pass priority
Guttersnipes ability resolves, you gain priority, you pass priority
Your opponent gains priority, again they can choose to cast their counter, eventually they pass priority back to you
As long as it wasn't countered your Bolt resolves. You gain priority after it resolves and can cast another Bolt if you want to.

If at anytime your opponent casts their counter the following is added to the previous steps:

They have priority, they cast their counter spell, they still have priority and pass
You gain priority, at this point you can choose to cast more spells if you want to, eventually you will pass priority
The counter spell will resolve, your Bolt will be countered, you gain priority and can cast more Bolts if you want to

A step or phase doesn't end until both you and your opponent have passed priority and the stack is empty.
As you point out Swift Silence is best against Storm decks, and other decks that have multiple spells on the stack at the same time (like Hive Mind)

116.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.
116.3c If a player has priority when he or she casts a spell, activates an ability, or takes a special action, that player receives priority afterward.
116.3d If a player has priority and chooses not to take any actions, that player passes. If any mana is in that player’s mana pool, he or she announces what mana is there. Then the next player in turn order receives priority.
116.4. If all players pass in succession (that is, if all players pass without taking any actions in between passing), the spell or ability on top of the stack resolves or, if the stack is empty, the phase or step ends.