"The best thing that financial regulation could do would be to forbid the publication of quarterly results,."
That'll never happen
Already has in London. Listing rules used to require a minimum of half yearly financials, and at least a trading update every quarter, the quarterly updates are now entirely optional. Some companies choose to do this, but there's no requirement, and a company can be compliant with two sets of results a year.
AC is correct that this reduces visibility, and some companies (including one I worked for) can go from boom to bust in less than six months. But quarterly reporting didn't make that any more obvious. If management are clear and communicate well, I don't think anybody will sell out just because there's no quarterly results. If they aren't clear and don't communicate well, would you then trust their more frequent updates?