Unless this is what Amy Schumer wishes to do I can't see her having the time to do it. From what I understand she is quite busy with her stand up career, and her acting career. But if she has said that she wants to do it, then sure why not, it might be interesting to have an actual celebrity do this show for a change.
Amy Schumer not only has the look of a Bachelorette star, she also holds the same values as evidenced by her comedy routines. Not only do her values align with the show, her popularity would generate many viewers and make the season more successful. Schumer would be beneficial to the bottom line.
Yes, I do think that Amy Schumer should be the next Bachelorette. Casting her would be a dramatic and remarkable departure from the typical cast of that show. That choice would attract a massive amount of new viewers that had never been interested in the show before simply do to the fact that she is a smart and clever woman.
The Barchorlette should be someone that is not famous. One of the primary appeals of a show like the Bachorlette is the fact that the people shown do not come to the show with a pre-established persona, and the audience meets the contestants as the show unfolds. Having a celebrity as the central character removes some of what makes a show like that acceptable.