Participation rates are important to a nation's health. Our Social Security system, for example, is funded by a two-part tax on workers and on their employers. If fewer people work then there are less funds flowing to Social Security, which is important since it is not a funded program but a pay-as-you-go arrangement. Genreral tax revenues would be lower as well and, of course, GDP.
In his famous book, The Wealth of Nations, Adam Smith makes his point about the importance of having more people at work, very early in the very first chapter of his treatise when he lays down the foundation of the causes of a nation's wealth:
...this proportion must in every nation be regulated by two different circumstances: first, by the skill, dexterity, and judgment with which its labour is generally applied; and, secondly, by the proportion between the number of those who are employed in useful labor, and that of those who are not so employed.
Source - An inquiry Into the Nature and Causes of the Wealth of Nations by Adam Smith page 2 Gutenberg e-book edition
So Smith focuses on skills (human capital), health, experience and managerial efficiency, thereby scooping by more than two centuries the thoughts of many management gurus, as well as touting the importance of having more people at work. Of course we should not take this to mean 'child-labor', although some nations do.
One thing we should also admit is that the extra drop in participation rates in this cycle also has something to do with the cycle itself. Not all of the forces are structural and some are reversible. Teenagers have dropped out of the labor force more than adult men or women. For some it is a logical reaction to endemically high rates of employment. For that group capital formation that substitutes capital for a lot of things like entry-level labor has probably been responsible for some of the job losses.
We need to distinguish between supply and demand factors. There is also the issue of wages which have been less attractive. For older teens the decision to not work may have been a decision to get more schooling, since the probability of unemployment was high, the opportunity cost of more education was low. Since the largest hit here (from falling participation rates) and the only dramatic one is for teens I'm not so sure how important it is especially given the historically high rates of unemployment (which are even higher now) for this group. In other words how much worse off are teens not looking for work than looking for it and not finding any?
The trend in the US to having proportionately fewer people working is a problem with long-run ramifications. It's a problem for Social Security and for the federal deficits since having proportionately fewer people working means also fewer are paying taxes. However, it is wrong to cite this as a problem that has developed in this recovery. These participation rates have seen some extra-normal drops in the recovery, yes. But the big-picture problem is not this additional small cyclical drop. The problem resides in these much longer multi year and in most cases multi-decade trends. Are people just waking up to that? The trends now show that women's participation rates are no longer rising (and have been pretty flat since the mid-1990s), that male rates are still falling (since the 1950s) and that teenage participation rates are very low (having peaked in the late 1970s).
So why is this suddenly an issue for this recovery? It is an issue for the economy at large and is it another example of the sort of structural change the US economy has undergone that is not for the better. These are trends we should seek to reverse. We need to draw people into the labor market. We need to do things that will make people want to work. If we are going to really spread health care benefits to everyone we need to have as many working to help pay for that as possible. Some are looking to implement policies that will make people HAVE TO work.
We should also look at policies to incent US firms to bring jobs back home. Tax policy plays a role in helping to move US firms offshore. A poor reading of economics and a poorer understanding of the gains from trade has encouraged the US to allow developing countries to peg their exchange rate to the dollar at presumed parity levels that are far too low. Too many countries have run nothing but trade deficits or surpluses for a decade or more. The US last current account surplus was in the 1990s! Our globalization policy is one place to look, but only one. There are many places to look to find remedies. The problem is not just that workers have passively stepped to the sidelines but that policies have actually encouraged that. And in that I refer to decades of Republican-Democrat policy initiatives. This has been a multi-decade bi-partisan SNAFU. Or if you prefer SNAPU: Situation Normal, All Politicked Up.