Reference is the answer. Below, the [a] examples with
on, tell us the speaker is, say, pointing to a calendar.
These days could be next week, last week or even next month or next year. In the [b] examples, however, the speaker is making reference to the present.
[1a] Flowers bloom on these days (here).

<demonstrative pronoun>
[1b] Flowers bloom these days.

<nominal adverb>
[2a] He's very busy these days.

<nominal adverb>
[2b] He's very busy on these days (here).

<demonstrative pronoun>
We keep sending cards
on those days: the unoffical days during the year. Not these days now, at the present time.
All the best.
