Without checkpoints a competing blockchain starting of the genesis block with a simple 7% difficulty growth per switch would be at the same length as the current blockchain. And just be running at ~ 300GH/s.
It would help if you learned how Bitcoin works. "Longest chain" doesn't mean highest block height it means the chain consisting of valid blocks with the highest total cummulative difficulty. Your chain with 7% difficulty growth every 2016 blocks would never be the longest chain. There are no shortcuts to the longest chain. The current longest chain is ~2^70 hashes worth of work. The only way to make one longer would be to do more work.
In other words you are saying that if two chains started with the same hashrate and one chain mined at this rate constantly (2016 blocks per 14 days, or 4032 per 28 days) while an other one alternates between this hashrate and double the hashrate (thus creating the first 2016 blocks in 7 days and then 28 days thereafter, or 35 days per 4032 blocks) the later chain would be valid even if this is shorter since it has a higher "cumulative difficulty"?
So you are saying that an attacker with sufficient hashrate (e.g. a company or gov with access to a huge batch of next-gen asics) could just fork of an old block and create a new valid shorter chain as long as cumulative has rate is higher???
Yes.
Here's a thought experiment for you. Imagine that the day Satoshi launched Bitcoin someone forked the blockchain, right from the Genesis block. He's been mining, on a tiny computer, since that day. On his chain, the difficulty never went much above 1, because he's the only miner - but his chain still produces one block every ten minutes. He's been doing this since day 1, and his blockchain is about the same length as the real one. It varies from time to time - sometimes his chain is a couple of blocks longer, sometimes a couple of blocks shorter.
Today, his chain is a couple of blocks longer than the public chain. Today, he broadcasts all his blocks to the world.
In a naive world, his 313631 blocks would be considered longer than the official chain of 313629 blocks, and every client on the planet would immediately have a block reorganisation, and accept his chain as valid.
But Satoshi wasn't naive. In the real world, his chain is worthless, because a block mined at difficulty 18 billion is considered to be 18 billion times more work than a block mined at difficulty 1.
Of course, there are all sorts of other reasons why the attack wouldn't work - you can never have a block reoganisation that goes back past the last checkpoint, and anyway, the average block interval on the public chain is significantly less than 10 minutes due to rising hash rate (so in reality the public chain would be longer in terms of block height anyway). But I hope this example helps you see why Satoshi designed it this way.
roy
