You are confusing function and implementation. Technically "get their transactions mined" is having a piece of data written to the chain. You are correct that

You are confusing function and implementation. Technically "get their transactions mined" is having a piece of data written to the chain. You are correct that in Bitcoin there is less incentive to store old blocks. But in chains crafted to store data for a long time there is. I am stopping this discussion here because you are too negative (almost aggressive) for my liking. But it will be an interesting thread to read again in 20 years when all this has played out.