Depending on where you are in a trend, the breaking of a short-term trend line, for instance, could set up an opportunity to add to an existing position when the trend resumes.
Also, forgetusername's point on false positives remains critical. Breaking trend lines is only a useful if it's right most of the time.
My advice to anyone who wants to be an enterprising investor (i.e. put more time into investing and try to achieve higher returns) is to read Ben Graham's The Intelligent Investor. Instead of trading based on the emotions in the market, invest by choosing great companies that are bargains.
As for false positives, nobody reasonable will tell you that they don't exist. But again, there's a difference between short, intermediate and long-term trend lines. Even under the most unfavorable scenarios, anybody with a modicum of knowledge of trend lines would have been out of the market before the 2008 crash and back in the market by early 2010 because major trend lines were broken. Incidentally, I was one of those people.
As for your advice: there's nothing wrong with fundamental analysis. Although many people fail to make money using it (just like technical analysis), it's worth noting that quite a few savvy professionals use fundamental and technical analysis together.