Is Proof-Of-Work simply a decentralized clock?
Yes, PoW is a decentralized clock not just for tying information to a specific time (a timestamp can do this perfectly fine) but to prevent spam attacks on the blockchain itself.

The question comes up, how can you add data to everyone's ledger all at once continuously and efficiently? If there is a single tx at a time queue system then things will be unbearably slow.

If the ledger is open for everyone to add verified transactions then what's to stop someone from just adding transactions on transactions and filling up everyone's node? 

PoW exists to solve this problem by creating something like a flood gate that allows only a set amount of transactions per time. The difficulty aspect of PoW exists to adapt to the changing nature of computing power against the network.


  The clock has an interesting property - you can tie data to its ticks, simply by making the data the input to the SHA. A solved block is nothing more than simply an event that happened exactly at the tick of this clock.


This is so an attacker can't just use the same verified data to add blocks and blocks of transactions. Think of a block mined by the miner as a one time use token that let's the block be added. 


  An analogy might be looking for the largest known prime. You don't need to tell anyone you decided to find one, you only announce when and if you actually find one. Your participation makes finding a solution a possibility, whereas if no one ever looks for the largest prime, it will never be found.


This portion isn't entirely correct. For you to test if a block you've mined is correct (because mining is entirely a guessing game) you need to ask the network if the block is valid. More than likely the node you just asked will say no and you begin the search again. 

Although I should note that the amount of failed attempts is not factored by the difficulty algorithm