The difficulty was designed by Satoshi to balance the network and guarantee equal access to new peers, preventing malicious third parties to control the network, filter transaction and obtain the generated coins too easily.
The PoW is a mathematical proof that someone spent resources to gain the generated coins. If there was no PoW, an organized entity with a lot of resources, e.g. a botnet or an ISP, would spam the network with transactions that drive interest to them.
In particular, for larger transactions (1), we need to be particularly sure that Alice (malicious spender) does not issue a transaction to Bob, which sells goods, and then spams the network with transaction to merchant Charlie or to themselves to fraud Bob.
Answering (or trying to)
Consider that Bitcoin is totally decentralized and distributed systems suffer the concept of time, which is not absolute. If you have questions on that you should post on SW Engineering. I'll just say "without a certification authority you can hold a message forever". And Bitcoin refuses certification authorities that can be hacked/bribed/forced-by-government etc.
Satoshi needed to design a system so that sequential transactions could not (that easily) be rewritten (2).
Suppose that Bitcoin nodes just accepted the block with the largest PoW every 10 minutes.
The very problem is: look it not from the perspective of the whole system. Look it from the perspective of my Bitcoin-qt client bootstrapping right now from void.
How can my client be sure that nobody is retaining blocks? How can my client be sure about the network size judging from the input of other malicious peers?
Satoshi expected the network to grow and the computational power along with it. With more mining nodes, a larger number of blocks would hit the difficulty treshold in less than 10 minutes.
From the perspective of a lonely node, which is the very concept of peer-to-peer networks, the target is not to identify the block with the largest difficulty, which would be difficult if peers try to hide information, but look for the longest chain
The longest-chain principle does not prevent Alice completely from rewriting a transaction. It makes it so expensive that, at least for grocery purchases, it's worth following the rules than cheating.
And is the very reason why peers require 3 or more confirmations to consider a transaction final.
(1) Bitcoin was designed in order both to buy grocery and real estate. Of course, it's not that loss a double spend at the grocery
(2) Rewriting a transaction, in the scope of a blockchain, means that if transaction occurred at block
100, replacing every block from