Is the verb form for "2nd day" more flexible than the one for "2nd time"?

Thank you once again, Califjim, for answering my previous question about the correct verb form for "1st time, 2nd time ... last time". This leads me to ask another question. I have written the sentences below.

(1) Today is the second time I have eaten three hot dogs in a row. (correct)

(2a) Today is the second day I have eaten three hot dogs in a row. (same verb form as in (1))

(2b) Today is the second day I am eating three hot dogs in a row. (an alternative form when used with "day")

There are no doubts about (1). Some of my non-native English speaking friends and I have heard both the present perfect (for a present action) and present continuous (for a future action) used by other people when "day" is chosen instead of "time".

I don't know why "day" allows for a more flexible word form than "time" in general. Please answer my answer. Your opinion will help me understand this concept better. I really appreciate your help. Thank you.