Here's why:
* "As do" is a conjunction introducing a clause that parallels a previous clause.
* Conjunctions generally don't require a comma unless there is a series of items or an introductory phrase.
Example:
* "He loves to read, as do I."
When to use a comma after "as":
* When "as" is used as a preposition: "I saw him as he walked by."
* When "as" introduces a dependent clause: "As the sun set, the sky turned orange."
Let me know if you have any other grammar questions!