Why do you assume the requirement of t->inf for an exponential model to fail?
I don't know why you are insisting so hard on your "exponential growth will fail" thing. Yes, of course it will fail, if will fail much before infty because there is an upper limit for difficulty, otherwise it would not be computable. Furthermore, why do you call it "failing"? We will see saturation, but no "failing".
That's how saturation (or, in your terms, "failing") looks like:
http://home.arcor.de/wetec/rechner/cladekurve.pngI see no saturation on the Bitcoin difficulty graph. Not even a clue.
http://bitcoin.sipa.be/speed-small-lin.pngHeh, because exponential systems cannot continue unfettered. People keep posting TGB mining calculator saying, "Look, Look! Look what the difficulty is going to be, you'll never break even!!!" without giving a moments thought to what the predicted values are and what would have to realisitically occur to support them. The point is, that the foundation of everyone's "IT WILL NOT ROI" claims are flawed because they're implying a continual exponential curve/model. What SHOULD be used is a Sigmund Curve, or S-Curve.
As to why I call it failing, because that's what uncontrolled exponential growth systems do. They fail, as in fail to be exponential over time. Either the phsyical system fails or the mathematical model no longer represents the physical world. Take your pick. It has nothing to do with the arbitrary upper limit of difficulty, but the tangible/physical requirements to support an exponentially growing difficulty.
The problem is that we *dont* know what's going to happen, but anyone familiar with mathematical models will realize that an unchecked exponential curve is not it. We are not going to add 14PH of equipment in the next 30 days, 28PH in the days following that, 56PH in the 30 days following that ad nauseum. I recognize this, and I would reckon that you do as well. It's the inability of the system to operate in this matter that opens up the possibility of reaching a positive ROI if the consumer makes educated predictions and assumes a sizeable level of risk.
That said, I'm not going to continue my diatribe since I'm driving this thread way off topic.