I am having trouble coming up with a use case for RSA or DSA. It appears that ECC is better in every way.
Is this true?
I am looking for cases where RSA/DSA is superior to ECC, not where it is used for historical reasons.
There are three use cases where RSA beats common ECC algorithms, such as ECDSA:
Signature with verification frequent or/and by low-power devices. The verification cost of $n$-bit RSA with usual public exponents is $O(n^2)$, but the verification cost of ECC-based signatures is $O(n^3)$ (using usual algorithms). Together with simpler math, that's why RSA can be way over 10 times faster for signature verification at usual security levels, even though it must use a larger $n$ for equivalent security level.
Similarly, encryption by low-power devices or/and with decryption comparatively rare.
RSA is thus a good choice (and indeed still the dominant one, I believe) for signing public-key certificates; beside inertia, in the internet domain that's mostly for reason 1 (certificates are verified often), but in the Smart Card and payment industry reason 3 adds up.
Additional arguments for RSA (vs ECC) are
We next examine some conjectures about the NSA’s motives in its PQC announcement (..)
The NSA believes that RSA-3072 is much more quantum-resistant than ECC-256 and even ECC-384. (..)
Note: this answer does not touch use cases where ECC is preferable, or its virtues.
If practical quantum computers become a reality, the larger bitlengths of RSA keys would make them more quantum-resistant than their ECC counterparts. See section 5.4 of this Koblitz & Menezes paper