Rick Berman thought it was a bad idea to have two Treks shows on at the same time--
That's not true. He and Michael Piller were the ones pushing the studio to do a TNG spinoff while TNG was on the air and the studio was flat-out telling them they would never produce a Star Trek spinoff. They finally gave DS9 the green-light. Then, once they saw that two Trek series at the same time could bring in the viewers, that's when the studio got greedy and asked Berman and Piller for a new Trek series to replace TNG and air concurrently with DS9.