Thats not really what they're for though that have the effect too. Most of their usefulness is that they prevent a dos attacker from filling up bitcoin node's disk space with long runs of low difficulty blocks forked off low in the chain.
e.g. you start off with difficulty 1 blocks at block 0, now mine-able by the millions by a single asic _MAYBE_ a chain that starts off that way could eventually turn out to be the longest so absent the checkpoints a node would happily follow an endlessly long chain of them.
Instead of checkpoints, client could hard-code a MAIN_CHAIN_MIN_POW variable. This would be the PoW of the main chain when that version of the client was released. All clients wouldn't need to agree on a value. It is just a spam protection value.
Clients should download headers first and only commit blocks to disk that are on a chain that has PoW higher than the hard coded minimum.
Clients should respond to "inv" messages containing unknown block hashes by sending a "getheaders" message rather than asking for the block.
If the block extends your main chain, you will be sent it.
Peer sends: "inv" containing unknown block
Send to peer: "getheaders" with standard block locator (send at most once per inv message received)
Peer sends: "headers" with new blocks on it's main chain
Add these headers to header tree
If the main chain is extended and the main chain has PoW greater than MAIN_CHAIN_MIN_POW, request those full-blocks
They also make is so that an attacker who has complete control of your network (and thus can prevent you from hearing the longest chain from the honest bitcoin network) from putting you on a fake (low difficulty) isolated chain unless they can also trick you into running replaced software. With the checkpoints such an attacker hast to have a ton of mining power in order to continue the chain.
No matter what happens, the longest chain will always have more PoW than the longest one when the client was writen, so the best chain is guaranteed to have more PoW than MAIN_CHAIN_MIN_POW.
The client won't consider itself synced unless it is on a main chain with PoW that exceeds that value.