This word got has been confusing me for a long time. Is it against the rules of English grammar, because got is the past tense of get? Why do I never hear people say it this way:
I get to go now.
In this case "got" implies an obligation.
The above sentence states that a person -must- leave.
The above sentence states that a person -may- leave.
A great blog post on this topic can be found here, referencing OED, Merriam-Webster, and The Cambridge Grammar of the English Language.
The sentence above states that a person was able to go [somewhere] previously.
The sentence above states that a person will be able to go [somewhere] in the future.
Because I got to go is the colloquial form for I have got to go. It should not be used in a formal manner. The have got(in this case) is used to show necessity or obligation. Saying, have got is a little stronger than saying, must.
While @dotsamuelswan posted a great discussion, he does not directly answer the question: "Why do I never hear people say..."?
I DO say this, and I have heard it said, usually when able to leave a boring meeting prior to the meeting getting over.
But you don't hear it said often because it is somewhat rude, implying something like, "Ha! You have to sit in this rotten meeting, while I am free as a bird!"