Some entrepreneurs are willing, but most funders are even less willing. A pitch that you've found some important, but uncommercialized, recent scientific or technical advances that you see a market niche for can be well-received. A pitch that you're going to make some significant scientific or technical advances as part of your startup's R&D effort is usually seen as way too much risk: a VC does not want "major scientific advance" to be in your critical path. The result is that the significant R&D has to happen elsewhere (often academia) to produce the stock of not-yet-commercialized results that startups can build on, rather than being produced by the startups themselves, since they can't have significant/risky R&D in their critical paths. Even Google, for example, only got funded after significant R&D work had been done by the founders in grad school.
Seems less true in biotech, where VCs are willing to fund substantial R&D budgets, perhaps because the [breakthrough -> patent -> license] ecosystem is better established there; the tech startups using the breakthrough/patent/license pipeline seem to verge on patent trolls more than real R&D outfits.
I don't think it's just analysis, unless your definition of "analysis" is impossibly broad. The other big problem is, once you've built your wondrous technical solution to medical records, or income tax, how do you break into the market?
Normally you would partner with some hip new entrant to (or at least, small player in) the medical or governance market, who isn't too invested in the status quo, and persuade them to use your solution via a combination of favourable pricing and the promise of a competitive advantage. But these fields are so far from being competitive that you just can't find such a partner.
I agree with you that they can, but I think the point of this essay is that startups can't solve these problems on their own, using only technology and chutzpah. In order to solve "health care recordkeeping" you have to get governments and large companies on board with the process. You can lead a horse to water, and all that. There are going to need to be a lot of people at the table, and for the most part a startup isn't going to have the political juice to make it happen.
Government may be incompetent, inefficient and slow, but at least they won't cut corners on security. For sharing tweets or something a startup can get the infrastructure done pretty quick, for something more serious (eg tax info) you really want a proper security team and proper insurance and legal advice.
VC's and advisors need to provide a platform to give startups those tools. For security using Google AppEngine or the Amazon cloud, combined with automated penetration testing tools, combined with some kind of cheap application security testing (does it exist yet?) might get enough of the way there, but would you really trust something so flimsy, run by two kids out of college who are working it out as they go, with your serious data?
You don't appear to know how security really operates in federal government software. They hire Booz-Allen-Hamilton for millions of dollars to come in with 200 consultants and produce a massive report declaring their software meets all "certification and accreditation" requirements. This document then goes on a shelf somewhere and government workers continue to email all kinds of PI data around in Word and Excel attachments because the software is so obtuse it's the only way they can actually get anything done.
There are such things as intractable problems, but payments, health care recordkeeping and government are not among them.
I do like the fundamental point of the post, though. There should be more attention paid by startups to serious problems.