I had forgotten about the timestamp overflow issue, but that would be the kind of hard fork Bitcoin would need if it would ever need one.
That kind of hard fork doesn't necessarily have the same problem that most other hard forks would have, though. At some point it would be completely impossible to progress on the old chain. If the fork activates at that point, there's no actual chain split, old nodes will simply be stuck on an old block.
In practice such a hard fork would be more similar to a forced soft fork.
Thinking about the timestamp overflow issue a bit further, it could have been implemented as a soft fork by exploiting Bitcoin's time warp bug. By my calculations this could extend the lifespan of the existing chain by some 240 thousand years.
However, after the activation of BIP113 in 2016, a time warp exploit is no longer a viable option as there's no way to do make timelocked transactions with a far-future timestamp spendable at the appropriate time.
But that part could be addressed with a forced soft fork at worst. So my point still stands ("tis but a scratch!"): Bitcoin will "never" need a hard fork.
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touché
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