This is a nice way to cut costs for your clients, albeit your solution has a single point of failure - FACTOM servers. Still some gov and corporate entities may be interested in using your service.
What I did not immediately understand after looking at the paper is why you need your own coin and your own chain?
Can't FACTOM be a subscription-based service where you hand out API keys to your clients to push the hashes to your servers?
Decentralized autonomous applications for the most part require their own token, if the actions of one party in the application obligate the protocol to provide services.
So let's use Factom as an example. At first, it would seem that anyone placing an entry into Factom could use Bitcoin to pay for that entry. But that means there would be a Bitcoin transaction for every transaction in Factom.... That would bloat the Bitcoin blockchain just as much as putting hashes directly into the Bitcoin blockchain, and it would require a Bitcoin transaction fee for every entry PLUS the Factom fee, so that fails as a solution.
But what if you use Bitcoin to purchase a bunch of entries. That would solve the bloat problem and the cost problem. A user could buy say 100 or 1000 entries in Factom, then use them up within Factom, then buy some more, then use them, and so forth. But now we have to figure out who the user buys those entries from. Is there a special owner of Factom? Or could just anyone sell these entries? And if just anyone can sell these entries, then why buy them from someone else? Why not just buy them from yourself?
So the way that Factom allows the selling of those entry rights is to issue and support our own token, the Factoid. Servers and auditors that keep the system running are rewarded Factoids for maintaining the system. Those Factoids can be converted into Entry Credits, so anyone holding Factoids can in fact provide a "Store Front" service for Factom users. The "Store Front" can accept Bitcoin, convert Factoids into Entry Credits, which get assigned to the public key of the Factom user buying those credits.
The User never has to see a Factoid. The User can pay Bitcoin (or even dollars) to a Store Front that in turn provides the User Entry Credits that can be used to put entries into Factom.
In other words, these Factoids represent an potential obligation of the Protocol to provide a limited amount of processing (i.e. adding entries into Factom). Factoids can be freely traded. Anyone with Factoids can use Factom, but more importantly, anyone with Factoids can allow someone else to use Factom.
An application coin simply represents a limited obligation of a Protocol, rewarded to someone for providing support for the protocol. Distributed applications will almost always require a token if the application requires something more complex than a simple fee for service to drive the application.