In a nutshell the current payment rails are expensive because the system is debt/credit based and so each party involved needs to contribute to the cost of insuring and settling the debt. Lightning OTOH has all transfers fully funded from positive balances of funds and this is workable because, as @dugsbodymentions, most people just want to hoard bitcoin and some proportion of those hoarded funds will be put to work essentially earning a yield in the lightning network.
So essentially it will work for the exact reason that @dugsbodythinks it wont.