Seems to me like the electric power grid is an already existing, efficient energy distribution mechanism. Converting waste heat to electricity is probably a lot cheaper to retrofit than adding a new distribution network to places that don't already have one.
To my knowledge there's no really effective way of converting low grade waste heat into electricity. Basically all heat-based electricity generation today relies on being able to boil water into steam to spin a turbine. But with heat pumps and district heating, you can recover useful amounts of energy even from quite small thermal gradients. That's why things like room temperature sewage and waste heat from data centers can be useful to these systems even though they couldn't be used to generate electricity.
Also, if you rely on local heat pumps, you still need to take the energy from somewhere. Taking it from the air is fine in warmer climates, but in colder climates the efficiency of air-source heat pumps starts to become an issue when it gets colder. You can extract heat from deep underground, but that doesn't universally work in densely populated areas because the ground doesn't contain infinite amounts of energy and it's possible to extract more than it can sustain. So, in cold climates there's definitely a use case for distributing heat using water pipes, with or without local heat pumps in every building (see the sibling comment about 5th generation district heating systems).
Thermodynamics prevent you from turning low grade heat into electricity with anything resembling reasonable efficiency. Moving the heat around on the other hand it reasonably simple.
