OK, I can tell you why they want it. It is not really sneaky, although I understand it makes you nervous, because all such documents, tend to have identifying info in them and can therefore, be a risk of living and doing business. That said, you likely have a condo agreement, that contains rules you have agreed to, including prohibitions, required actions, and required maintenance fees. Should you fail any of your obligations, they can sue you, get a judgement and satisfy the judgment, which often depends on having your SS number. Also, if they have a contract with the major credit bureaus, they are required to report any late payments, typically, and to do so they need your SS # ***** maintained by the credit bureau.
Unfortunately, as you have surmised, there is no law to suggest they are required to destroy the information. If you'd included that requirement in your agreement with them that they could access your credit score, then you could enforce that. But because your SS# ***** ***** also in your sales contract and / or deed, it is likely that they have copies of it many times over. That said, if they negligently kept same and it was stolen, you could in theory hold the condo liable for negligent bailment or similar, negligent invasion of privacy perhaps, etc. But until there is actual damage, I am not seeing a legal cause of action yet.
What they can not do is access your credit file again without your permission, if you didn't give them prospective permission at some point in the past.
Your best best to prevent damage from any ID theft is to regularly monitor your credit file yourself - you will know who has been looking at it and if the looker has not been given your permission, you may want to look into it.