To me, this is starting to sound like a very interesting iOT hub to tie various sensors together and then either host or upload the data to the web. The CPU certainly has the horsepower to do both, the OS gives it the potential to make use of a lot of inexpensive hardware. If the MCU is more accessible re programming, all the better. Is it a replacement for Teensy? Not at all, at least for me.
There is no way that you can run anything but casual DAQ on that platform because the timing cannot be controlled the way it can on a close-to-metal MCU. The ADC on the Teensy is flexible, versatile, offers 2 simultaneous inputs, etc. A single high-resolution DAC, well-defined PWM outputs, and so on further features allow for a pretty bomb-proof swiss-army knife re: data acquisition.
But, does the average consumer of this hardware care about achieving precise timing, good ADC results, and so on? It wouldn't be the first time that inferior hardware reigned as the market went on to adopt a less expensive platform. If I was beagle bone, I'd be much more worried about the Pi because I'd argue that the Beaglebone is much harder to differentiate to the average consumer. Similarly, the folks at Propeller may have a very interesting architecture but the maker market settled on AVR instead. From a manufacturer point of view, that is what these Pi projects are about - capturing market share and hopefully becoming a dominant platform for that chip maker to milk in the future, short term profits be damned.
Pis may be a competitive threat to Teensy or they may be a potential symbiotic partner, where the Pi takes care of some of the really hard to implement OS features (i.e. USB host mode, Wifi access, web server, etc) that do not require precise timing but a very flexible OS that benefits from decades of software development to allow robust performance, while the Teensy takes care of the very-had to implement things on a PI - precise DAQ / ADC, etc. What would worry me about a symbiotic relationship is whether that market (DAQ, etc) is a big enough / profitable enough one to make the work worthwhile. Consumer expectations may become totally warped by hardware prices that can only be described as unsustainable.
However, the sheer scale of Pi sales is pretty eye-opening. The question going forward is how many will still be in use in a year instead of lying in a drawer like my Maple board. Dumping tasty hardware on the market is one thing, putting the time into making said hardware accessible, reliable, etc. is an entirely different task and one that hardware manufacturers typically fail miserably at. Whether it's the lack of longevity (i.e. see the multitudes of 'paradigm-shifting' kickstarter projects whose makers have moved on to other things) or the lack of supporting its users (mbed, maple, diligent anyone?) Teensy is differentiated majorly by its ease of use and its support.
There is a reason that so many folk gravitate toward Teensy - great hardware coupled with excellent product support (arguably, best in industry, at least at the maker price point).