Complicated topic; a couple ways of approaching it.
One way is to say this: All countries (and regions) have periodic downturns. When this happens you either have fiscal flows from richer to poorer regions (the US does this), or you have currency devaluation (the EU prior to the Euro did this). After the Euro, the EU was still reluctant to have straight up fiscal flows (if the EU worked the way the US works, Germany would straight up fund Greek unemployment benefits). But with a shared currency, currency devaluation was also not possible. This left only one answer: So called internal devaluation. The standard neoliberal textbook answer is "don't ever do this, it's slow, terrible, and doesn't really work", but Greece had no other options. (Krugman is quoted at the link; in this he speaks for the neoliberal consensus.)
You ask why you shouldn't think of Greece is a deadbeat; the answer is the same reason why you shouldn't think of Alaska as a deadbeat, or the north of England as a deadbeat (both relatively poorer regions of larger nations which are net recipients of government transfers); because they're people suffering from an economic downturn largely beyond their control, and they need help. Greece didn't need (or deserve) loans, they needed aid...or a devaluation. Since aid was politically impossible, and devaluation legally impossible, they got loans. Which they couldn't pay back, which forced them to make cuts which deepened the problem. To the surprise of no one, really, but what else could be done? Even Krugman never identified a politically and legalally feasible alternative.
Another approach is to focus on your question "If Greece was given a clean slate, would it be a healthy, productive and growing economy?" The answer is "yes of course". Until Syriza came to power Greece was running a "primary surplus" (that means their budget balanced if you don't count interest); that means that if they simply defaulted they would be, economically, fine. Greece doesn't (or didn't, but we'll come to that in a moment) need to borrow to fund ongoing government operations; they only need to borrow to fund repayments of the money they already borrowed. And again, they were forced to borrow, because the options that would normally be open (aid or devaluation) were closed to them.
(Note: Greece hasn't run a primary surplus the last two months because tax receipts crashed on the election of Syriza. Syriza ran against some of the more onerous taxes, and people stopped paying them on the assumption that they would soon be repealed, or at least unenforced. Ironically, this means that the election of Syriza has made the bargaining position of Greece's Syriza-led government much worse; the last government could credibly tell the markets to jump off a cliff, but the current one needs to continue borrowing to avoid a crisis. Not the first political party to be hamstrung by their own election promises, but it's rarely so severe.)
Anyhow, when you say "Maybe that ought to be the reality for Greece?", what you're really discussing is a devaluation, where a nation collectively realises they aren't quite as rich as they thought, and scales all their expectations down. A salary that might have stretched to a new Lexus now only stretches to a new Toyota, or whatever. Devaluations are normal and healthy; southern European countries devaluated their currencies over and over and over again in the post WWII years. Greece should have done that at the start of the global financial crisis; they should probably do that now.
There's just one problem: They can't do it, because they're part of the euro. Or rather, they can, but rather than it just being a matter of the drachma/deutchmark exchange rate shifting a bit, and everyone's drachma salaries being worth less, while all the tourist's pounds and marks are worth a bit more, with everyone's mortgages, employment contracts, pensions, etc. being left alone, Greece now faces the reality of an internal devaluation, where everything has to change in a brutal, grinding process. (Edit: Devaluing the currency would also decrease the loan burden; they could just print drachma to pay back the German loans. Which they can't do now, because they don't have the drachma. My point is its all linked; Greece has much less control over their finances than we would expect a "real" country to have, and all the obvious answers that countries all over the world have used and continue to use are closed to them. Personally, I struggle not to be sympathetic. The US and the UK don't—in fact, can't—face a problem like Greece faces, because they still have printing presses.)
(Again, US states face the same issue, but the US has a strong federal government that transfers enormous quantities of money between regions. The EU, in comparison, is tiny. And incompetent. And (arguably) dominated by Germany.)
TL;DR: Joining the euro removed every existing easy or painless way to fix the problem, but didn't add any new methods. You can blame Greece for joining the euro all those years ago, but once they did, the problems were set in stone. Calling them deadbeats now isn't really accurate, but worse, it's pointless.
Ninja edit: Or, of course, Greece could exit the Euro. But that cure might be worse than the disease. Then again, there may no longer be any other options. We live in interesting times.