Future perfect is also used to indicate a past likelihood, one that has consequences for the present or future:
- "As you will have already heard, the gym will be closed today"
- "You will have noticed that we no longer have a convertible."
I can't come over tonight. <present>
I couldn't come over last night. <past>
Read more here.
 Click English Grammar Lessons
 "... why couldn't we also claim that present gerund is used for building those two tenses?"
Use a present infinitive to express action at the same time as or later than that of the verb.
Use a perfect infinitive to express action earlier than that of the verb.
Ex: I prefer to stay right here.
(Present infinitive to stay.)
Ex: She would have liked to join you.
(Present infinitive to join.)
The perfect infinitive combines to have with the verb’s past participle: to have kicked, to have
written. It shows action that occurred earlier than that of the verb.
Ex: We now know human ancestors to have existed millions of years ago.
(Past infinitive to have existed.)
Ex: My father would like to have been an actor. (Perfect infinitive to have been.)
See also Perfect Infinitive. Fowler, H. W. 1908. The King's English
=>Becuase a gerund cannot function as a part of a verb. Gerunds are either subjects or objects.