Not sure the second regression works, especially the log(K/A) part. A (and therefore K/A) can clearly be negative. For example if S(T) tends to be greater than S(t) when RV(t..T) is less than IV(t), then A will likely be negative. Since K is always positive, log(K/A) would be undefined. Good general idea though. I think many people are running quite similar regressions. The other difficulty is, on a daily sampling interval, that you have a complex overlap structure (due to t getting one day closer to T each day) to your regression.
25D RR, 25D Fly, and ATMF, all priced in Vol, completely describe the standard-tenor FX option pricing curves. Nearly all FX options are quoted in those terms, not in actual prices-in-currency. That is the main use of the 25D RR. SK10 is mostly used (again, AFAIK) as a rule of thumb -- a mnemonic for "in your head" calculations/estimates. It effectively linearises the near-the-money vol curve, making it look like the hinge loss curve and thus easy to calculate from. "Skew" trading/modeling indicators, on the other hand, are usually more complex decompositions of the vol curves/surfaces.
Of course it does not work because it's not a regression. It's an equality ("=" vs "~") where you solve for B for a given date (everything else is known, implied vols and strikes). Both K and A are absolute strikes (e.g. 95% and 100%), so the log would be defined
One of the better written paper regarding Skew presented in "Journal of Derivatives" What Does Implied Volatility Skew Measure? https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1618602 " What Does Implied Volatility Skew Measure? This paper provides theoretical guidance and empirical analysis aimed at differentiating among implied volatility skew measures. Industry analysts and academics use a variety of measures, but most have little formal justification. I find that most commonly used skew measures are difficult to interpret without controlling for the levels of both volatility and kurtosis. Many ad hoc measures fail to meet the conditions for a valid skewness ordering. My preferred measure is the (25 delta put volatility - 25 delta call volatility) / 50 delta volatility; among the measures considered, it is the most descriptive and least redundant." ... It concludes that "Volatility skew measures relying mostly on liquid options might also be more relevant as statistics for trading strategies that are actually implementable. One such measure is (25 delta put volatility - 25 delta call volatility) / 50 delta volatility, which emerges as the preferred skew measure based on the theoretical and empirical analysis presented here."
There are two separate problems and they go beyond this particular problem, of course. One is the problem of the overlapping periods in the options data when comparing to things like realized volatility. You can correct the errors and R^2 by using several statistical methods (like Newey-West procedure) but then any results with lower R^2 should be taken with a grain of salt. The other one is the problem of fixed maturity (call it "trombone" or "telescope" problem) in the options data. Personally, I get around that by looking at interpolated sliding window tenors in implied volatility.
Well there are many ways to "skin a cat", and trading perceived mispriced skews and curve slopes within the term structure of an underlying, or temporarily misaligned curve shapes between two or more highly correlated underlyings is just one of many ways to generate alpha. But it's difficult to put on a pure play skew bet even in just one product given the inherent risks of assuming a large RR position, ratio spread, X-mas Tree, etc. There are so many hazards. Vega, gamma and floating skew risk come into play if the underlying moves toward your shorts or longs. If you have large position inventory in strikes with heightened levels of 2nd and 3rd order greeks such as Vomma, Vanna, or Speed a violent move in the underlying and volatility can dramatically effect your P&L and overall risk profile in unpredictable ways. Staring at the behavior of the options of one underlying all day, it is easy to spot the floor and ceiling levels of curve steepness and skew over a short time horizon (intraday or intraweek), much harder to spot the long term trend - which is completely dependent on the price direction of the underlying. Now try and do this with a portfolio of skew bets across many underlying instruments. You have skew basis trades between positively and negatively correlated products, mixed in with a large number of independent high probability curve skew/slope bets in non-correlated underlyings to try and keep the variance of your portfolio down. I would imagine that you would be constantly adjusting and rebalancing your position to attempt to mainly capture the IV mispricing between strikes and avoid as much exposure to vol and gamma risk. You would also have to figure out a way to beta-weight your total skew risk, so you could hedge your overall exposure to a "risk off" market correction when all or most instruments and their skew behavior usually show high correlation. Not something that could be easily automated either. Despite all the bs you have to deal with, there's big money to be made in this sphere. Now I just have to convince a deep-pocketed futures and spread/pair trading firm who know little about options that this can be done.
There are several ways to be purely exposed to skew. Some of them can be approximated using particular option books that need to be dynamically adjusted. The question remains : is it worth the cost (wrt reward and risk associated)?
Probably best to incorporate a vol and directional bias (which is the same bet in my opinion) in your skew bets, it's unavoidable. And you can amplify your skew and vol bets with calculated put/call ratio trades rather than a high maintenance vega neutral RR that needs to be readjusted every week, but which could probably be automated.