No we can't have a cryptocurrency without blockchain mostly because of the addresses' balances. If block 1 contains a transaction that Bob sends to Alice 1
BTC and Alice wants to hold that bitcoin for a year she can't based on your topic. She'll have to spend it before the block that contains her transaction gets deleted. If she loses the block, she can't prove she own it.
I announce that I have mined 50
BTC back on 2009 on block #1000. How can you confirm that I mined them if you can't look the coinbase transaction of that block? I don't get how you're imagining a cryptocurrency without a ledger.
There are too many forks in this system, but what if we approve the fork that is most accepted every time?
There is something more important than the use of a fork. The demand. Bitcoin was the first one, all the others were not. Even if litecoin is faster than bitcoin, the majority doesn't recognize it that much. Who's the second person who stepped on the moon? Do y'all know him?