Whether or not it is flawed in practice depends on dynamic the risk exposures really are. Many factors or indices used for style analysis actually require dynamic trading to maintain - so you could potentially have a fund that trades a lot while still generating a return series that can be be modeled out of sample with static exposures.
One relatively simple approach for what you are trying to do is to use the Lasso (discussed in the paper). This will achieve your goal of reducing factors as they coefficients will be shrunk towards zero. Another more complex option would be to use Bayesian regression with informative priors to estimate factor exposures. For example, you might have different priors on the exposure to SPY of a long/short equity fund vs. a merger arb fund. Kruschke, author of Doing Bayesian Data Analysis, also showed an example of "robust" regression where the errors are assumed to follow a t-distribution. Both of these approaches are pretty straightforward in R.
Finally, if you do you want to explore dynamic exposures you could use a state space model to estimate time-varying parameters. This is a bit more complex to implement, but one of the R packages that is useful here is dlm. The package's author has written a book: Dynamic Linear Models with R. There are also various slides from Yollin floating around online demonstrating how to estimating time-varying beta exposures using dlm. You might want to check out Understanding Hedge Fund Alpha Using Improved Replication Methodologies by Chen & Tindall, which I believe a number of these approaches.