This is a great thread, hence my first post here.
Generally speaking, unless you have a super high lautering efficiency, like, approaching big factory rates above 95%, you won't extract husk tannins, undesireable levels of protein, etc. For most homebrewers like me, the very best I can do is about 90% on a great day.
The tradeoff here is between leaving extract behind, vs. paying a price for getting more extract out. For most brewers, you won't be paying the price since you don't lauter efficiently enough in the first place to get your final runnings extract level low enough.
There is however a much more significant reason to consider your mash thickness carefully. This has to do with wort attenuation relative to mash thickness.
The rule of thumb is: "All other things being equal (and this is a very big wild card), a thinner mash will yield a wort that will attenuate more than a thicker mash". There is a lot going in in this statement. Your pH will be different, your temperature ramp may be very different. But if you can control those, then the above statement is true. The reasons for this are complicated and have to do with the amylase enzyme family - one is a relatively thermodynamic enzyme, the other is relatively kinetic, and they have solubility differences as well that a thicker mash can accentuate.
Some of the posts above talk about using 1.25 or 1.3 quarts per pound of malt. This is a pretty thick mash, and will yield a wort that ultimately will maintain some residual body in the finished beer.
You'll see a big difference if you mash in using, say, 1.5 quarts per pound of malt - the mash would be a lot thinner, easier to stir, probably won't pull air. And, all other factors being equal (again,assuming your mash pH is the same, your temperature ramp is the same, etc.), compared to the thicker mash example from above, will yield a wort that attenuates further - the finished beer will have a bit more alcohol, and a somewhat lower apparent extract. This may or may not be what your're looking for - this can make a very big difference in how the final beer tastes, especially when using very hot (highly modified) US malts when trying to approximate an overseas beer style that has some residual body.
There is a big range of mash thickness you can try. There is nothing sacred about any ratio of water to malt. Ultimately, you have to decide if your mash thickness is appropriate for the taste profile you're looking for. This post does not advocate a thicker or thinner mash. It's just to make you aware that changing the mash thickness will in fact change your flavor profile, and provide a tool for folks who want to try to tweak a recipe.