Hello, everyone.
Today I have a question about the usage of 'to-infinitives (which function like nouns)' and 'gerunds'.
Please read these sentences below.

1. My hobby is playing the piano.
2. My hobby is to play the piano.

Both 'playing (a gerund)' and 'to play (a to-infinitive)' function as nouns.
However, #2 is not natural English. (This is what I've learnt here in this forum.)

3. My plan is taking my son to the zoo.
4. My plan is to take my son to the zoo.

I don't think native speakers would actually say #3. #4 is more natural in this case in my opinion.

5. I hope to see 5jj and Rover in the near future.
6. I've decided to go to America and see Barb_D, SoothingDave and TheParser.
7. I would like to talk with bhaisahab and emsr2d2 in person.

I somehow feel #4, 5, 6, 7 have something to do with 'futurity'. (The actions described with 'to-infinitives' will(might) be performed at some point in the future.)

8. Please remember to take out the trash tomorrow.
9. I remember taking out the trash.
10. I regret to inform you...
11. I regret informing you...

Again, #8 and #10 have to do with 'futurity'. #9 and #11 refer to the 'past' actions.

So, I've come to the conclusions:

'To-infinitives' are more to do with 'futurity'.
'Gerunds' are more to do with 'present' and 'past' actions.
(I know there are lots of exceptions.)

Are these good enough reasons why #2 is unnatural?