Why is sharding not possible with a distributed blockchain? Hi guys I've been reading a lot about the problem of scalability in crytocurrencies and how to run a full bitcoin node is not a possibility on a mobile device for example, as a result we become relient on centralised 'power nodes',

My question is: what is it about the datastructure which makes sharding the full blockchain across many lite devices not possible?

For example node 1 stores blocks 0-100, node 2 blocks 101-200, etc. A node wishing to verify some transaction can then just keep pinging nodes until they connect with a node which is storing the data they're interested in.

Apologies if this is a noob question, still got a lot of learning to do!
Your question is a little unclear as it only talks about storing, and not really about validating the entire blockchain. Storing is actually not the problem. Recent versions of Bitcoin Core support crude pruning and work is underway to make it more flexible. 

However, to be truly trustless a full node still needs to download and validate the entire history of all blocks (even if deleting that history seconds later). This is what David Schwartz answer comes from: you need a complete history to know whether a transactions was NOT in it.

So in that regard pruning doesn't help mobile devices much.