> If that's the case, why doesn't the NSA publish Suite A algorithms?
The math on whether you find the vulnerability before somebody else does is very different when you employ as many cryptographers as the NSA.
They also have concerns other than security vulnerabilities. It's not just that they don't want someone to break their ciphers, they also don't want others to use them. For example, some of their secret algorithms are probably very high performance, which encourages widespread use, which goes against their role in signals intelligence. Which was more of a concern when the Suite A / Suite B distinction was originally created, back when people were bucking use of SSL/TLS because it used too many cycles on their contemporary servers. That's basically dead now that modern servers have AES-NI and "encrypt all the things" is the new normal, but the decision was made before all that, and bureaucracies are slow to change.
None of which really generalizes to anyone who isn't the NSA.
A lot of the Suite A algorithms have also been used for decades to encrypt information which is still secret and for which adversaries still have copies of the ciphertext. Meanwhile AES is now approved for Top Secret information and most of everything is using that now. So publishing the old algorithms has little benefit, because increasingly less is being encrypted with them that could benefit from an improvement, but has potentially high cost because if anyone breaks it now they can decrypt decades of stored ciphertext. It's a bit of a catch 22 in that you want the algorithms you use going forward to be published so you find flaws early before you use them too much, while you would prefer what you used in the past to be secret because you can't do anything about it anymore, and the arrow of time inconveniently goes in the opposite direction. But in this case the algorithms were never published originally so the government has little incentive to publish them now. Especially because they weren't publicly vetted before being comprehensively deployed, making it more likely that there are undiscovered vulnerabilities in them.
If we assume for the moment that there are no ulterior motives:
Cryptography is the keeping of secrets. Obscurity is just another layer of a defense in depth strategy. Problems occur when security is expected to arise solely from obscurity.
If that's the case, why doesn't the NSA publish Suite A algorithms?