The only monetary use case Bitcoin is not capable of is that of the privacy-centric coins, but privacy enhancements will end up being added to Bitcoin in one form or another (aggregated signatures & Mimblewimble are possible future such privacy enhancements). Maybe there'll always be a better privacy coin for enthusiasts, but I suspect Bitcoin will eventually do privacy more than well enough.
I'm thinking more in terms of smart-contracts and utility tokens / currencies (eg. Namecoin) -- but fair enough.
I'd love to see a proper smart-contract platform growing atop of Bitcoin beyond what its currently capable of, but even with promising concepts such as Simplicity I remain slightly reserved about whether all of this should take place on one and the same blockchain. Even ignoring turing-completeness, which, in my opinion, is an inherently bad idea for smart contracts. But that's a different discussion.
Privacy is also an excellent example -- keep in mind that MimbleWimble is currently bound to become a cryptocurrency in its own right, due to fundamental differences in transaction and blockchain structure. I concur that for most people Bitcoin's privacy will be "good enough" though, especially given potential future improvements.
Very true. Case in point: The unquestioned trust in fiat currencies.
The biggest challenge for Lightning to me is security. I'm probably exposing some ignorance here, but it seems to me that having unencrypted private keys in the memory of permanently online machines is risky. Maybe there's a way of mitigating that, or perhaps that mitigation exists already.
Technical challenge yes, but the general populace cares surprisingly little about digital security. So in terms of widespread adoption I see usability as the bigger concern.
In terms of security I don't think LN nodes are much worse off than regular hot wallets. Even with an encrypted wallet file, if your machine is compromised an adversary will only have to wait for you to unlock your wallet, leading to the same result. Keep in mind that LN is for active spending and not long term storage after all.
Given time I could imagine hardware wallets becoming LN capable as well. While there will be some compromise in terms of security -- after all this will require hardware wallets to sign transactions without human interaction and therefore a re-thinking of potential threat models -- I don't see any technical reason that would prevent the isolation of private keys from the rest of the operating system, as is the case today.