Berman certainly thought it was a bad idea to have VOY and DS9 on at the same time, at least. At least they only did DS9 when TNG would be off the air in a while.
Berman and Piller had approached the studio around TNG's fourth season to do a TNG spinoff. It was the studio who didn't think they should air two Trek shows simultaneously. It may be that Berman didn't think doing VOY was a good idea at all
. I remember in an interview shortly after DS9 premiered, the interviewer asked Berman when it would be time to create the next Trek series, and Berman laughed it off as a joke and said something to the effect of that being pushing it too far and implying that he wouldn't have anything to do with it (I think this was in one of those Cinefantastique annual Trek issues). It wasn't long afterward that VOY (and UPN) was announced. The studio had done a complete 180 degree turnaround in its opinion of having two Treks on at the same time. They became convinced that Trekkers would eat up anything with the name Star Trek on it and wanted a show to replace TNG when it went to movies (and, of course, to be the UPN flagship series).