The final cut of the 9th episode of the Tesla Motors Club Podcast, featuring Chad Schwitters, the former president of Plug In America, is now available. You can watch it now on YouTube or listen to it on all major podcast networks.
There is nothing in the NEC that prohibits it, although you may be subject to local codes. Nothing in the NEC requires wiring larger than #6 to be in conduit (SE and SEU cable is a good example). You may be thinking that because until recently, NM-B cable was not commonly stocked at anything larger than #6. 4/3 has been available in NMD90 for Canada, but was not listed for use in the US. There are now larger cables - for example, 2/3 - that can be used.
The biggest problem with using NM-B larger than #6 is that NEC 334.62 requires you to use the 60 degree column for ampacity, versus wire-in-conduit which can typically be used at the 75 degree column. (The wire itself is rated at 90 in both cases, but you have to consider termination temp limits too.)
For example, if you want to wire an HPWC for a 100A breaker, #3 wire-in-conduit will work, but not even NM-B #2/3 will not (it's limited to 95A and you need 100A). The added expense of having to use a bigger cable starts to make a big difference, and conduit is cheap enough.