There are a lot of hard problems startups try to solve which no one cares about. That's the trap to avoid.
Fixing something hard does not inherently make your company valuable in the marketplace.
Fixing a hard problem does not automatically make your company more valuable, but failing to fix a hard problem will never increase the value of your company.
While this theory sounds good, it is disproven time and again by initial half-baked versions of sites that then go on to take off. Just check the original launch of YouTube, Digg, facebook.
Also, a HUGE idea coming from lean startup way is to invest very little in marketing until you have a product users like. You don't need to get one million users to tell you a product sucks. Often, 50 would do. Now if you are saying that 50 users writing off your product will doom it for its lifetime, the problem isn't the lean way it's that your market is too small. YouTube guys had very poor reaction to their initial site.
"because our metrics show no one wants it"
They have little idea on how to use metrics. Don't blame lean startup ideas for that.
ie. What lean startup would do is put up a button that looks as good as your best competitor can put up. Then see how many people click on it. What you measure is action until the click, not the engagement after the click to draw conclusions about the demand for that feature. Now if 1000 people are clicking on the link but only few are using it, chances are your product sucks. Take that insight and work on your product. Just one small example.
failing to fix a hard problem will never increase the value of your company.
If you are saying that you have to solve really hard technical problems to increase value of your company, I full disagree. Just look at the web2 companies that took off.
Craigslist did not take off because it solved a huge technical problem. Craigslist also has a lot of value as a company.
It is easy to disprove the theory if you get to cherry-pick your examples. Would you like me to list the thousands of other companies that had a couple of poorly implemented features masquerading as a "beta" that were stomped into dust by others who worked a bit harder to do the job better?
Btw, I don't consider using some of the most popular web2 properties as an example to be cherry picking. I'm curious to see your examples nonetheless.