Because economists tend towards some consensus of what the "true" model of the economy is, they will also give answers in unison that are based on an application of that model to any given historical situation. Simply, there is an enormous demand in economics to be Right, even though all macroeconomic models exist on shaky ground. Claims made about the macroeconomy are not falsifiable through experiment; all they have to go on are theories and a limited amount of historical data. Even if a policy works once, or for a period of time, its effects are obscured by being in a constantly-changing environment. As someone who got a bachelor's in econ - I graduated feeling that micro was a far more worthy and well-reasoned topic than macro, and to this day I struggle through people's macroeconomic statements. As I've studied other topics over the years I've come to think that most of those statements are politically motivated and commandeer an edifice of theory for nefarious purpose; it's far easier to evaluate the power structures the words represent than the words themselves.

Pernicious aspects aside, the history field has gradually shed the reliance on deterministic thinking while economics embraces it; more than one interpretation of historical sources can be truthful at any given time, even if their conclusions disagree. Broad topics like the Depression, with many possible causes, are amenable to similarly many angles of interpretation. There isn't a "one right answer" so much as "a few likely ones."

The blog's assertion of a consensus is overstated. The study's author, rather than saying that the view was basically mainstream among economists, said that it was controversial among economists:

On top of the profession's lack of agreement about the genesis of the Great Depression, there is a disagreement about the effect of the New Deal. In fact, the economists in the sample are almost evenly divided on the question of whether or not when taken "as a whole, government policies of the New Deal served to lengthen and deepen the Great Depression." The consensus among historians is that the new Deal did not lengthen and deepen the depression.

The actual numbers for economists were 27% agreeing generally, 22% agreeing with provisos, and 51% disagreeing generally; three quarters of historians disagreed generally.

Note that both blog authors seem to hold libertarian beliefs, assuming their Wikipedia entries are accurate, and would have an inbuilt bias against government intervention in the economy, as well as the innate human bias of seeing their own profession's opinion as more worthy than another's.