Cool idea but this could backfire if someone ended up getting a bunch of characters with steep learning curves. A fixed set of starting characters allows the devs to give access to the most beginner-friendly battleborn.
A slight modification could fix that though, perhaps you could always start off with characters #1, #2, #3, #4, and #5 but get 1-2 random characters. So Player 1 may get characters #1, #2, #3, #4, #5, #1337, and #9001 but Player 2 might get characters #1, #2, #3, #4, #5, #777, and #7331.

