You're right, we'll likely still have some debt. But most of that debt will be due far out. With few exceptions, most companies incur debt to finance their operations. The only reason Chemtura is in BK is because the financial mis-management of the prior management team and the economic downturn made paying off their near term debt difficult.
Perhaps they could have avoided BK, but that would have involved them unloading assets at fire-sale prices, and severely hampering the future growth of the company. Now they have what they didn't have before: management that knows what it's doing and time to get the company's finances in order, including an asset(s) sale at a more reasonable valuation. This may well be a textbook case of how the BK process is SUPPOSED to go.
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