> The blockchain won't "halt" at overflow, it will have validation problems.
These "validation problems" will be quite serious. For example: it will be possible to produce a chain with a bigger chainwork, and pass it to the old nodes.
Which means, that the chain can go forward for the new nodes, while being perceived as a constantly reorged, by the old implementation.
And then, the question is: do we want to design a new soft-fork in a way, where it would be seen as constantly-reorged chain by the old nodes?
> The overflow doesn't automatically stop the chain.
It will, because overflowed timestamps from 1970 will be rejected by all old nodes.
> At that point there are no more valid blocks that can be appended to the chain.
As long as the chainwork won't overflow, you can always reorg the old blocks. If that reorg will be deterministic, and accepted by hashrate majority, then it will be seen only by old nodes. New nodes can see a stable chain, always going forward, beyond 0xffffffff.
Anyway, it will be just one-bit increment per 136 years.