Would it be possible to create a blockchain that uses only X+ active blocks?

Would it be possible to create a blockchain that uses only X+ active blocks?

Every blockchain has a beginning, the Block 0 or also known as "Genesis Block". But wouldn't it be possible to have a blockchain or a coin, where only the last 1000 blocks are saved and 1001+ get deleted automaticly?

My question is, because it would save very much problems.

1. Full anonymity: Yes, you could save 1001+ blocks but if you need only 1000 blocks, you can delete the others. So at a specific point in time, you could create a real 100% anonymous cryptocurrency because the other blocks would no longer exists.
2. Saves disk space: It does not longer need much space to download the blockchain. Also that means, that blocksizes could be bigger.
3. Finally, this is one of my favorite points. When people know that they can use a blockchain where they don't need to download a blockchain for 10 hours before being able to using it, more people would and that would mean that the blockchain would be more decentralized and so it would be more secure.

Now the negative or dangerous points, that I'm not sure about. So currently, the "computer" goes through all blocks and checks if the transactions are correct and if the user x had enough coins to send to user y. That's possible through algorithms that are not reversable. I still wonder if you could hack through 1000 blocks. Next point is, that a 51% attack would be much more likely to happen. But maybe you can combine the coin with POS. And maybe you can not save only 1.000 but 50.000. But combined with ethereum and bitcoin, it would still be 10x less blocks AND the blocks will still be deleted so the disk space keeps at stable at a point. I mean, the basic problem is not the block amount, but more the danger if one person/institution/group holds the most power. And then it would no longer matter how much blocks there are, they'd be successful in any coin.

I'm interested in knowing about why that wouldn't be possible. And I really hope that that's not a basic blockchain thing and I'm embarassing myself, lol.

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