First of all, I'd just like to state that any model that isn't based off scarcity is a fantasy because reality itself provides multiple limits on us. The only limitless dimension we can ever hope to experience in our lifetimes is our imaginations. The most simple illustration of this is time, in which we all have a limited amount and since all of our lives are built upon a limited and scarce amount of time, we can never hope to build something that is limitless on top of it. Logically, it makes no sense.
However, I'd like to address this abundance model specifically:
The Abundance Model. A promise of something specific from someone specific made valuable by its redemption in real production. The value of this type of money is defined by the promised redemption in goods and/or services. As such, this type of money is promises of an indefinite number of non-uniform commodities in indefinite supply and, unlike the limited quantity "coin" concept of money, the total quantity of these credits in circulation does not affect their value, because the value of a credit is defined by what its issuer will redeem it for in real goods and/or services. Examples are: business-to-business barter credits, customer rewards, travel points, discount coupons, mutual credit systems."
In this system, there is scarcity as well, namely the specific person and the specific good or service. For example, if 100 people have promises that a local carpenter will build a porch for them and that person dies, all those people who have this promise now have a worthless promise because that person will never be able to fulfill their promise. The main abundance in this model would be the amount of people defaulting on their promises.
Abundance is an illusion, scarcity cannot be escaped. The sooner it's accepted, the more practical solutions that can be devised based off of reality.