Or am I missing some critical function or feature the Basic stuff provides?
When the Basic Stamp came out (1993?), things were a lot different; there was really only one "hobbyist" electronics magazine left (Nuts and Volts); Popular Electronics and others had, by that time, started waning badly (and eventually disappeared). Hardly anybody was playing with discrete electronics or digital circuits, hobby robotics was nothing like it was (from what I can gather) during the 70's and 80's; really, the entire market was in a downturn.
The PIC, and soon after, the Basic Stamp - changed all that. It was really the "shot in the arm" the entire market needed.
While PICs by themselves were fairly easy to play with, the Basic Stamp opened things up to hobbyists who, up until that point, really only had a few choices if they wanted to create a project that depended on computer control. They could 1) interface with a PC (I am not singling out the standard clone PC here - I mean to indicate all popular computers of the time, such as the Amiga and Atari ST), 2) use an 8051 kit - homebrew or otherwise, 3) use a PIC.
In the case of option 1, you could control your circuits (usually via the parallel port, or some custom/kit 8255 PIA interface card on the EISA bus) fairly easily using assembler, C, or BASIC (usually a form of QuickBASIC); it was well documented and available. For options 2 and 3, you usually had to use assembler, although in the case of option 2, there were ways to cross-compile using C (but IIRC, the compilers weren't cheap).
Most people who were building electronic projects (just like today, actually) had little to no skills in programming; so the shorter the learning curve, the more likely it was to be adopted. You saw a lot of people interfacing their projects to PCs of all stripes, because the interfaces were typically very well documented (many books were written on the subject, especially for the IBM clones), and it was easy to use BASIC (if you were poor, GWBASIC, if you had some money, QuickBASIC) - as your skills grew, you could even add some assembler into the mix, either via "debug" or "masm". For most projects, that wasn't needed.
So - when the PIC came about, some developers embraced it fully; enough embraced it that some started to write small BASIC compilers for it (because while the assembler for PIC was simple, it was still not that fun to write in - and the assembler libraries started to get large and unweildy to a point - and probably other reasons that I am not privy to); a critical mass was reached, Parallax saw an opportunity (or they were formed for the opportunity? I don't remember the early history very well), and the Basic Stamp and PBASIC was formed - and people LOVED it.
Finally - a microcontroller that could be coded for in a simple language, that ran an interpretor fast enough so as to do a variety of projects and functions (that had once been relegated to complex IC logic systems in some cases) that was accessible - and more importantly - cheap (by the standards of the time). Most other systems either required an outlay of cash (for a real 8051 system, or other 8-bit system like a 6809 or whatnot) that was not insignificant, plus if you wanted to embed that into your own design, you typically had to at a minimum add your own EPROM system (oh, and you needed an EPROM programmer, and maybe a UV eraser, etc). A lot of dollars, a lot of complexity, and that was before you even got to the coding. Only the most hardy of souls delved into those worlds (and fortunately it was enough - otherwise, we wouldn't be here today).
With a PIC, you could get everything you needed for a few dollars, and a programmer (that you could plug into your parallel port) only cost a few more dollars (if that - if you had junk parts you got it for free); it was really revolutionary. The addition of a simple bootloader code and interpretor for BASIC, which Parallax initially provided, boosted the cost of the PIC, but even so, a dev enviroment was still cheap (and the Stamp was cheap too), compared to what you needed before (and let's be honest, those kits were a huge step up from the costs and complexities of say, a KIM-1 development kit!).
There was a lot of buy in, and a lot of educational institutions were involved, and now many are stuck with a lot of components of what (to them) appears to be a "proprietary, one vendor" system. Where have we seen this before?
Remember the "Apples for School" programs of the late 70's and early 80's? Schools heavily invested (and got discounts - which I am sure Parallax provided to educational institutions for their products as well) in Apple IIe computers during the 1970's and 1980's. As time wore on, so many schools got stuck with a bunch of aging Apple IIe computers because of the investment in, well, a proprietary, one-vendor system; just like we are seeing now with Parallax.
Perhaps, just like the clone PCs did (and Microsoft - can't forget them, as much as I would like to), a more open system like the Arduino can help institutions like schools break out of this closed mold. It should be easier this time around though, especially if a company or supplier like the OP can create an Arduino Nano-like 0.600" DIP format controller that can slot-in seamlessly into the Board of Education, BOEBots, and other "Stamp Only" carrier board systems; it could possibly allow for an easier transition to the real Arduino platform, a staged phase-out over time, rather than an abrupt and costly switchover (which would have to include class curriculum changes, etc).
Hmm - perhaps the author of that Arduino Beginners book should write a teacher's edition, with tests and quizes and such?