Three channels, because they are three different messages
A LinkedIn connection note has a hard 300-character limit set by LinkedIn, so it has room for one specific fact and an ask. A referral request goes to somebody who already works there and has to ask without assuming they owe you anything. An intro email needs a subject line, because an email without one does not get opened.
Nothing is pre-selected. Guessing on your behalf would quietly hand you a 300-character note when you meant to send an email, and the draft is not interchangeable between the three.

