忙しい or other states of being (not limited to i-adjectives) have some duration for which the state remains. On the other hand, に stands for a pinpoint time during the date within the day.
I mean, a day in particular has 24 hours, that sounds like a range to
１４日 can be a time period that has width, but １４日に indicates a point in the 14th day. Moreover, ...
i-adjectives like やすい turn into adverbs via the rule
-i → -ku
やすい → やすく
早い → 早く
新しい → 新しく
The i-adjective やすい can attach as a suffix to the masu-stem of a verb like 分かる, but the result 分かりやすい is grammatically still an i-adjective and in the phrase
分かりやすく is an adverb for the verb いう (here in the form いえば). (Similarly, 早くいう "to ...
Let me show my idea to explain this really difficult question.
After the “(Absolute time)に” we basically expect something happening or something changed. Adjectives and adjectival nouns are just for describing status of something and that’s far from happening, that's probably why it doesn’t fit in the sentences like your example.
In order to grasp this ...
I think the confusion comes from the fact that both kind of words are labelled as い-adjectives and な-adjectives, creating the illusion or expectation that both types of words function grammatically in the same way, and that where you would use い for one type, you can expect to use な for the other. This expectation is not true. Let's compare both ...