Not very likely with a PoW implementation as the economics of the "coin" is what enables the "work" to get done (unless of course the mining is all government provided).
But with other low-cost consensus systems (and so far none have really being proven to be anywhere near as reliable as Bitcoin) the motivation could be the value of what else the system can provide (e.g. a decentralised "blogging" implementation) so assuming the cost to participate is negligible then the utility of the software platform could provide the reason for people to support the network (much like the motivation for running a ToR node).