The definition of work also leaves out many socially beneficial tasks because they don't provide a path to profit for a business. Planting trees in a park is definitely hard work, but not likely to generate an income source unless the market for such can be created via privatization.
Socializing with our elderly, teaching music to kids, gardening for people who are food insecure in our cities, and many more tasks could be considered "work" if they could only generate income. With our major needs provided by importing goods or robotics there is no need to leave so many disenfranchised while also seeking labor to perform socially beneficial tasks.
We only need to fund those tasks and those who wish to perform them with public money. Given that the federal government can create money as it needs it, such funding needs to originate there, but with local management to best evaluate need and benefit.