This pattern is used to single out one thing as the ultimate or only possibility, often in negative or critical contexts. It carries a nuance of 'that's all there is' or 'that's the most one can expect.' For example, when you say 彼にできるのは謝るくらいのものだ, you mean that apologizing is the only thing he can do (and it's not much). The pattern often implies limitation or inadequacy, but it can also emphasize that something is the extreme case, as in 夏は暑いのが当たり前で、冷房なしで過ごすのは無理なくらいのものだ (in summer it's so hot that without AC you'd think it's impossible). It is a spoken-friendly pattern, though with a slightly emphatic tone, and can be used in both casual and formal speech depending on the politeness level of the ending.