A severability clause has nothing to do with closing down the contract. Severability in contracts essentially means that the terms of the contract are not "all or nothing" -- they can be severed from one another. So if one of the clauses in not enforceable, only that clause will be thrown out.

Whether you want a severability clause or not depends on a bunch of factors. Sometimes people insist on clauses that are not enforceable -- that can be used to your advantage.