A particular hang-up the regulators have is explaining P&L and even relating it to capital. One use of delta-gamma-vega-neutral portfolios is to show how the movement of complex option pricing functions can only be imperfectly approximated using the function’s derivatives (e.g. the Taylor series), and that the slippage in the explanatory power grows the farther one moves away from the current state. Of course this is well known about the Taylor series, but enough regulators do not seem to get it. All this is to suggest that such demonstrations can be used to carefully temper the naïve regulatory expectation of explaining everything.
More generally, one can conduct numerical simulations using this framework to gain a keener appreciation of hedge slippage, a concept that is fuzzy among too many people. One can see how and when hedges slip, and, as you note, how profit opportunities disappear as risk factors are hedged. When I traded, I always conducted simulated hedging experiments before offering more exotic products, just to derive some comfort before betting the shop on them. Any decent finance school should offer simulated trading exercises as a normal part of coursework.