Just adding a little about the reasons, and some examples:
Reflexive pronouns want something to refer to reflexively. Contextually, the speaker is there, but, in English, the speaker has not put him- or herself into the sentence context without first naming him- or herself.
So you would never start with myself in proper English.
Well, almost never.
Putting myself in your place, I would not deliberately use this particular pattern unless I had a good reason.
You can (and should) be reflexive in an introductory dependent clause when the reflexive pronoun refers to the subject of the primary sentence.
... which brings us to what the speaker should have been saying in the first two examples in the question:
I would like to introduce myself.
Is a but fluffy, but not wrong. Going from there,
Introducing myself, I am a member of the xyz club.
To introduce myself, I would like to tell you about my hobbies.
But both of these feel forced. In English, it is acceptable and preferable to just jump in and introduce yourself:
I am John Brown. I am a member of the xyz club.
I am John Brown. Among my interests ...
(I think I could edit those into the answer above, but I'm not comfortable playing with other people's prose.)