Yeah, like once every 4 years... But anyway a faster coin will come around soon enough...
Not one based on the bitcoin algorithm. Litecoin is already too fast most likely.
The Bitcoin algorithm is not convergent when the highest latency (including all block validation time) bisection of the
hash rate becomes higher than the mean time between blocks.
What do you mean bisection of the hash rate? Difficulty is adjusted automatically so block creation moves toward the target regardless of hash rate. I think you meant bisection of miners, which would make more sense. But even that is problematic. How do you split miners mining coins into two halves? Mining, like Bitcoin, is decentralized.
E.g. if a chain has a 3 minute average block time an it takes 3 minutes for some half of the miners to hear from and validate another half, then most of the time a new block will be found in each half before it's heard about the other half's blocks and the two will form longer and longer forks, which take longer and longer to reorg between. The result is a partition with the halves not able to agree on the history of transactions.
At current transactions levels (which are only a portion of the maximum allowed) Bitcoin is already seeing multi-minute propagation in some cases.
Now multi-minute propagation is interesting, and something I hadn't considered for Bitcoin or Litecoin, so I can see your point. Invalid blocks do result currently with Bitcoin from latency of miners learning of found blocks elsewhere due to the network effect.
This problem should worsen as Bitcoin adoption grows and the network expands. So this could conceivably be a problem for Bitcoin, Litecoin, or any cryptocurrency with a block creation around 10 minutes or less on average. Mining invalid blocks is a waste of resources for miners, which would be a disincentive where there is supposed to be incentive. Frequently occurring invalid blocks also complicates trust in confirmations.
However, I think there is a simple solution. It's in everyone's best interest to know of a valid found block as soon as possible. This way work can start on the next block with minimal wasted resources for no reward. While it's not called for in the protocol I think there can be developed what I'd call mining block references or MBRs. This is simply one or more online resources (nodes or sites) where miners can report and check for found blocks. Since all miners (or a significant number anyway) would reference only a few nodes, polling say every few seconds, communication of found blocks could be near instantaneous regardless of network size.
The network effect exists now because Bitcoin is designed to be decentralized. However, smart centralization of some aspects, especially non-critical functions like this can be beneficial. Note this doesn't change the protocol. It's just a reference on top of how things already work. Satoshi's white paper says "When a node finds a proof-of-work, it broadcasts the block to all nodes." It doesn't say
how to broadcast that information to all nodes. I think optimization of that is easily accomplished with MBRs.