Can you expand on the DSA/ECDSA problems? One this I greatly dislike is having "only one option" of RSA. In my opinion, it's better to have a variety of secure algorithms available and that are well studied, so if a new attack emerges we're not completely hosed. Also, while I don't believe NIST is a mouthpiece for the NSA, I'm curious why they haven't proposed some alternatives to P-256, given some of the difficultly…
A lot of the problems with (EC)DSA are around nonce use. The k in ECDSA has the worst intersection of possible cryptographic randomness requirements: despite the name, it's not just "don't reuse me" (though that's disastrous too), it's also "be unpredictable and secret". An attacker that can reliably predict part of (let alone all of) your k has pretty much won already. The other issue is the failure mode: when this fails, it's not just easy to detect and exploit (well, full-k-reuse is easy at least), the attack also results in the key being entirely compromised. DSA is a no-good footgun. Contrast: EdDSA and friends, the recommendation in this document, is real hard to mess up.
I'm not sure what you mean by "I dislike having the one option of RSA"; this set of recommendations does not tell you to use RSA, it tells you the opposite.
Having multiple options is fine, but having multiple options as a recommendation for people writing cryptosystems is a disaster, and that's what this document is for. We've tried "agility". It was a bad idea. Cryptanalysis isn't hampered much by a set of recommendations. People are studying SIDH and LWE long before either is an everyday cryptosystem.
It takes a long time for NIST to make new recommendations, and I think there's a fair argument to be made that P256 isn't really broken enough to warrant a new spec yet? I mean, you can in fact write secure software that uses P256; if you've used a browser to hit Google today you probably already have.