Not really. FliteCharts gives you IFR instrument approach plates, a good idea specific to IFR, which is what these units are really about. But no, for the basic moving map, its the same as VFR, no FAA VFR sectionals, no FAA IFR low enroute or high enroute IFR charts.
It's not a bad idea to make it available. Not a big deal to me - that what an EFB is for. But I suspect that, in addition to the target IFR market, an issue is current database size and processing considerations. The map you see on screen is fairly small. Adding FliteCharts increases the requirements but not as much as a complete set of multi-colored they are really huge. As an example you can look at the difference between Jepp and FAA charts in Foreflight. The entire US in Jepp - approach charts, low enroute, high enroute, and Jepps; own brand of VFR chart, takes up less space than one or two FAA sectionals.
It is possible. The Dynon line does provide what you want (different target market), but in that case, the charts have to remain on a USB stick. They can't be loaded into the unit itself. Way too big.