According to this question the volitional form of i-adjectives is used quite often -- on a daily basis. But I almost never hear it. I almost see it exclusively in books (or written documents). And if it would be used in a dialogue it would almost always be used by a man.
On the other hand, I hear quite often adj-i+でしょう.
So my question is the ～かろう form that much used?
This form is classified as modern 口語 (as opposed to 文語), but it sounds old-fashioned nevertheless. It's not something we hear every day. We mostly see this form in fictional old person's speech (like in the original question) or in a few fixed expressions like 安かろう悪かろう. よかろう is often used by a pompous, old and/or noble person in fiction. If someone around you used よかろう in reality, it's likely to be a joke.
By the way, is that form really called the "volitional" form while the meaning is ～だろう? It appears similar to 行こう/見よう/食べよう, but the meaning is totally different.
