Feeless transactions are rather appealing to crypto enthusiasts, but they are problematic. The main problem being how consensus would be achieved. Bitcoin has a strong network because there is strong incentive for miners to uphold and maintain the integrity of the network.
Take iota, for example. Iota is offering revolutionary solutions to the IoT industry. The network runs on the tangle, not a blockchain. They offer feeless transactions. Naturally this would make it attractive to users, but this has no bearing on the functionality of the network. Clearly, running full nodes would require some form of incentive, but the founders predicted or expected people (and institutions) would want to run full nodes just to be a part of the project, and also to process and handle their own data and transactions. But this turned out to be rather optimistic. Iota suffers from a limited number of nodes. Of course in theory, iota solves the consensus problem. But translating theoretical work into something physical has always been a challenging task.
Is feeless txs the best approach to a crypto? And how can it be made to work? Other feeless (and more robust) solutions exist, like nano for example. It would be interesting to explore how they've achieved this.