Supercaps and discharge
Yes, you can use switching power supply topologies to slowly and safely discharge a large capacitor bank. These can be controlled to create exactly the load current you need. Basically every switching power supply has some DC intermediate circuit with a capacitor bank, exactly as you described above. 

Still, the remark from the comments seems to be limiting factor here. First you talked about datacenter usage, then you changed to a typical home.
Let's just assume an average consumption of 2kW during the 8h. This seems legit for home usage, but is way to low for a datacenter.  

\$ 2 kW * 8h = 16 kWh = 57.6 MJ.\$
This is the energy we somehow need to store in the capacitors.

\$ 57.6 MJ = E_{Cap} = \frac{1}{2} \cdot CU^2\$

I just checked at a big electronics distributor and the "best" solution I could find would be an 8.4 V supercap with 15 F.  

\$ C = \frac{ 2\cdot E}{U^2} = \frac{2 \cdot 57.6 MJ}{(8.4 V)^2} = 1.6 MF \$
Megafarad. Mega. Farad.
With the above mentioned capacitor with 15 F each this would just require... 100,000 peaces! With a price of ~15$/piece you can calculate the cost of this. And this calculation assumes that the switching power supply can discharge the caps with 100% effiency over the complete voltage range down to 0 V. Not likely.

And now let's not talk about a supply for a datacenter, right?