Is it practical to compensate full nodes in the Monero network? The nodes that aren't mining

The primary issue with non-Proof of Stake methods is the sybil attack, but requiring full nodes to already have a minimum amount of XMR mitigates this via attrition. 

As for what these staked nodes do can be anyone's guess. Perhaps only staked nodes are eligible to issue assets once MoneroAssets are possible, but getting them compensated from the block reward or other issuance schedule would promote both scarcity and network security.

Despite the dubious utility of masternodes in the dashpay network, it has achieved scarcity and demand for the token, and I think the core concept can be replicated before being outright dismissed