That first part... that's not how the spell works at all o.o
And that second part? That's exactly the common tactic.
I'm not sure what spell you're thinking of, but your complaint is perfectly wrong, as you describe the use of the spell as your assumed-wrong scenario.
Silence only has one save, at the start, and only if you casted it on a living being or an item held by someone wanting to resist it.
You can even cast it on yourself, or an object you're holding, with no save at all. Then move with the silence around you, or throw the item where you want the center of "silence" to be...
Even better to cast it on your melee-based ally, who'd then go melee the casters XD