Coal has the same optimization problems meeting the demand curve as renewables, but all that existing complexity is hidden when you plug the TV into the wall and it demonstrably 'just works'.
You have the same basic issue of keeping supply and demand in balance, true, but that doesn't mean that the problems are comparably serious or equally tractable.
The two big problems with wind and solar PV are that (a) you have no control over when you can generate electricity and (b) the variations are correlated over large geographic areas. To work round that you either need a very large amount of storage capacity (infeasibly large in most locations using current technology), or backup from a dispatchable generating technology (probably gas - not as bad as coal, but still not sustainable).
Solve the storage problem then wind and PV become much more interesting. Otherwise they may still make sense as a small percentage of the mix but they cannot be considered scalable.
Solar thermal goes some way towards solving the diurnal problem, but not the seasonal problem. Hydro is great because you can use it for storage, but most of the viable sites are already in use. Geothermal power is good for baseload, but has geographical constraints and isn't as green as you might think. That leaves nuclear power, or if that is considered unacceptable for political reasons, fossil fuels (as we are currently seeing in Germany).