Drawing a line through $0.06 and $2 is simplistic. It assumes that both $0.06 and $2 were properly priced. It also fails to consider that a minuscule amount of Bitcoins traded at both of those prices and also fails to consider the effect of all the other multitude of data points between them.
What if the $0.06 tick was a single scared trader who sold off a relatively small number of coins into a thinly traded market. Excluding this trader maybe the low of the day would have been 2x as high.
What if the $2 tick was saved from a lower tape by MtGox lag? In a perfect market with perfect access maybe it would have traded down to a buck.
Drawing another line through $0.12 and $1 on those days may look completely different. That is the problem with just picking a few data points (often the peaks and lows by "technical" traders). Those points have some value but they aren't "the whole story" and a few small events on those days (now given heightened importance) can significantly change the line drawn.
Linear regression attempts to discount the effect of those extremes by:
a) considering all data points not just two humanly chosen points which satisfy a conclusion you already had before drawing the line
b) consider the relative DISTANCE of each point from the overall trend. The ticks the furthest from their peers (outliers) have the least influence on the line.
Is linear regression perfect? No.
Does the chart in the OP predict the future? No (it simply says IF and ONLY IF Bitcoin continues the historical trend it will follow a random walk around this line).
Is it better than picking two points at random and drawing a line? Yes.
IMHO I think Bitcoin will hit a plateua at some point in the future simply because the infrastructure (hardware wallets, deterministic wallets, node efficiency, legal issues, service providers) haven't kept up with the growth. This will create a "bottleneck" of sorts on higher adoption and price but there is money to be made solving those problems and they will be solved in time. Obviously (if I am right) this is something that no statistical model could see or even claim to see. Growth would follow a trend line and then break the trend (significantly) for some period of time.
Still for the sake of argument lets pretend you "randomly picked and drawn line using two data points" was a perfect predictor of price on a long term scale. You still really haven't shown that the trend is unsustainable. Bitcoin is risky and there have been a lot of risk "hits" in the last two year (FinCEN, MtGox getting seized, SR closed, various exchange hacks/thefts, bank freezes by various Bitcoin related companies, legal notices by the state, etc). It is entirely possible that risk is discounting the actual price from the trend line (remember in that early trend prior to the $32 spike Bitcoin was pretty much invisible to law enforcement, governments, and traditional finance). So it is certainly plausible in the short term the increased risk would discount Bitcoin from the trend. You will notice that even on your "chart" the price is following the trend it is simply discounted. As Bitcoin gets bigger much of that risk will be reduced and you could see the price rise up to meet the trend line some years in the future. Simply put drawing a line across three years of data and saying it is broken long term is .... well silly.