Challenges to design high-density power inverter
The 'little box challenge' lower power density target of 50 W per cubic inch translates to just over 3 kW per litre, which is a more widely-used unit in the literature.

For a 3-phase DC-fed inverter for a motor drive application, in which there is very little energy storage requirement, 30 kW/litre, i.e. an order of magnitude beyond the 'little box' targed, has been demonstrated:

https://www.semiconportal.com/en/archive/news/main-news/110906-nedo-sic-fupet-inverter.html

To achieve the required low input current ripple (which equates to a low input power ripple) whilst supplying single-phase AC output power with its inherently pulsating nature, energy storage within the inverter is required (in other words, 1+1 = 2).

A good example of what can be achieved may be found in the following paper (2.75-4.86 kW/l, 94.9% peak eff., all-Si):

http://itohserver01.nagaokaut.ac.jp/itohlab/paper/2013/ecce_us/ohnuma.pdf

(Not all the efficiency figures match up and there's no photo of experimental hardware, but it's an example of something in the 'close, but no cigar' range for the LBC). There are a number of publications on this technique or variations thereof, allowing greater capacitor utilisation than the conventional 'bulk' DC link filtering approach, which results in a significant 'DC' energy storage overhead if low voltage ripple is required.

As evidenced by the 'Pareto Front' diagrams (see also detailed work by Kolar et al. of ETH Zurich), extreme efficiency and high power density don't necessarily go hand in hand, and whilst you can get some way by throwing more silicon (or SiC) at the problem, self-discharge and gate driving losses place an upper limit on this. See Infineon's CoolMOS C7 application note ('Mastering the Art of Quickness') for examples.

There are several trade-offs to be considered here - the increased losses (and therefore heatsink volume) of a higher switching frequency vs. reduced filter component dimensions, for example. All well-understood stuff. I'd suggest that the 'clever' is in simultaneously optimising the various design trade-offs and maximising the performance of the individual components.

The factor that's not an issue here is cost (or reliability, beyond a 100-hour test). On a 3-dimensional plot of cost per kW vs. efficiency vs. power density, I'd hazard a guess that a typical small commercial solar inverter is as far up the efficiency curve as possible for a strict cost limit, sacrificing power density in the process.