There is absolutely no prospect of drawing 72A from a "regular outlet".
As long as the feed to the house is adequate - and that level of power is within the range that MAY be available in many US residences, but not all, if would be possible to have a purpose provided circuit and outlet made available.
The closest that you will find available in a "normal" house is the feed to the range (electric stove), but even this is very unlikely to provide the power level required.
An internet search for USA range fusing provisions suggests 40A, 50A, and 60A in use in various installations. 50A seems common. A look at the fuses or circuit breakers on your house's distribution board will show you what the Range circuit is currently "fused" to provide. The actual circuit MAY be rated at slightly above the fuse rating, but probably not.
The relevant regulatory standard is often NFPA70 - this is non binding and optionally adopted in the US and may be adopted in revised form in a given area, BUT it's a good guide.
Here's a quick comment on US range wiring. Newer ranges may be 40A and older ones are apparently more likely to be 50A. They say
- 50 Amp Electric Range: Old range ovens require a 50 amp breaker because of the massive load that the stoves use for baking. Six AWG size copper or aluminum wiring is acceptable for this size circuit. If aluminum wiring is used, it has to be installed into a CU/AL breaker. This means that the breaker accepts copper or aluminum wiring. The outlet that the stove is plugged into also has to accept aluminum wiring if it is used.
Assume you have a 50A circuit. At 110 VAC that will provide 110 x 50A = 5.5 kW.
It's likely that if people are achieving adequate results with 8 kW then you can get the same result with 5.5 kW plus additional insulation and more care.
Kilns may be wired to allow the use of 2 or 3 phases. Elements are liable to be connected Phase-Neutral and not Phase-Phase. So technically it may ell be possible to supply a kiln made fro use with 2 or 3 phases from multiple circuits or outlets all supplied from the same phase. It is reasonably likely that such an arrangement would not meet regulatory requirements.
Kiln elements are liable to appear mainly resistive to 50 or 60 Hz mains.
You mention power control by switching earlier and later in a cycle - with kilns you will get acceptable results by switching whole cycles with on/off controls. This allows zero crossing TRIAC control ICs and much simplified control electronics.
Very basic zero crossing / random phase tutorial here.
Nice Fairchild zero crossing TRIAC controller application note AN3004. More detail than you'll want at present but a worthwhile reference document.