Hard fork without non-mining full nodes = weak network? This question is NOT intended to ignite diatribes. All of the discussion of a hard fork focuses on mining nodes; I have read nothing about the role of non-mining full nodes. So this is a sincere question.

The vast majority of bitcoin non-mining full nodes are running Bitcoin Core, and seem quite likely to continue doing so in case of a hard fork. That would result in a hard fork supported by (perhaps) enough mining nodes, but a dearth of non-mining full nodes. That strikes me as a weak peer-to-peer network.

The non-mining full nodes scrub/validate every transaction and every block, and these nodes are "Switzerland" inasmuch as they are not participating in the mining game. And then there are the more explicit benefits of thousands of non-mining full nodes: higher resiliency, lower latency, higher reliability, etc.

Hence my curiosity: if a hard fork resulted in a peer-to-peer network rich in mining nodes but lacking in non-mining full nodes, well, isn't that BAD? If it IS bad, why hasn't this facet of a hard fork been discussed. If it is NOT bad, by all means let me know what I'm overlooking.
It's not great, but non-mining full nodes are relatively inexpensive to operate, and if ordinary users start switching to that fork, some of them will bring their full nodes with them.  The network will get along okay with fewer.  If it really starts to be a problem, miners, exchange operators, and others who have a vested interest in the success of the fork, can fire up some full nodes.  

If ordinary users don't switch to the fork, then it's doomed regardless of how many miners choose it.  It doesn't do you any good to mine lots of a currency if nobody wants it.