While I am not aware of any firm definition for thin vs. thick mash, your estimates of 1.25 to 1.5 quarts per pound do seem close to the mark for an average range for most homebrewers. For many years I have targeted an average ratio of about 1.3 qt/lb, with great results. That being said, I do sometimes go as high as about 1.75 qt/lb, which is thin but not overly thin. I do this for certain batches where I do not want to sparge but wish to experiment with a no-sparge batch. There are some sources who have occasionally recommended ratios of 3 or even 4 qt/lb for various purposes -- now that is a thin mash! But people have had success with it.
With respect to beta and amylase and availability to convert the starches, etc., this is people will argue.
Many claim that a thicker mash results in a thicker beer, and vice-versa, and theoretically, this makes sense because in a thick mash, there is reduced capability for enzymes to move around in the mash, as there are too many other alien molecules like proteins, lipids, etc., in the way. On the other hand... people who have experimented with very thick mashes sometimes will get normal conversion efficiency anyway.
And on the thin side, theoretically, to take things to an extreme, if you were to throw a sack of malt into an ocean of hot mash water, the enzymes will be so far apart that there will not be much conversion happening. However, also, as I said, experimentally, some people have NOT found conversion to be a significant problem in ratios up to about 3 qt/lb or maybe even 4 qt/lb (which personally I have a harder and harder time believing). Looking at things in this way, indeed, your 1.5 qt/lb or my 1.75 qt/lb really does NOT seem very thin at all. So the definition for a "thin" mash is still up for debate. And if we use a more reasonable ratio such as 1.75 qt/lb, theoretically, the enzymes will have sufficient space to move around (not so many alien molecules in the way), AND will bump into plenty of starches to work on converting to sugars, so the theory here is that conversion efficiency can be improved by thinning the mash, as compared with a thick mash of say 1-1.25 qt/lb.
Overall, I think the pros of a thin mash (to a certain point, anyway, which I'm not sure exactly where it is) are improved conversion efficiency, and reduced need to sparge (like to make no-sparge batches), and/or for brewing in a bag (BIAB) this might be an ideal way to go.
And the reasons a thick mash might be recommended, and for which I myself still do them at ratios as small as 0.8-0.9 qt/lb, is for extremely high gravity worts or high alcohol beers where I want to sparge with a LOT of water so that I can collect far more sugars out of the mash so that I can boil for an extra long time (often 2-3 hours or more) to concentrate it all down to a specific gravity of say 1.090 or higher without sacrificing efficiency. Anyone who has tried to brew a 1.090+ beer with a non-adjusted mash and boil regimen has & will experience this phenomenon where you might expect an efficiency of say 75% but in the end you only end up with like 55% or in that ballpark. But by sparging extra and boiling for a very long time, you can keep your efficiency at a perhaps-desirable 75% or more with these high gravity batches. So this is the advantage of a thick mash here, that you can sparge more, AND are able to fit the whole mash into your mash tun!!
There is a homebrewer by name of Kai Troester who has experimented with hundreds of batches to gather scientific data to compare various mash parameters, and has shared his data and conclusions with us in the format of a "wiki" document. I have not read all of this site in detail, but I suggest that you or anyone very interested in mash science should do so, link is here: http://braukaiser.com/wiki/index.php/Braukaiser.com. Enjoy -- I hope you find the answers you seek which I do not all have stored in my own brain yet. Cheers.