The rumor has always been that Ridley Scott didn't want voiceover so he directed Harrison Ford to do a really shitty job. The truth is a little more interesting.
Blade Runner scripts have always had VO in them. I've read three versions and they've always had voiceover. The production was problematic as hell, though, and between finishing production and finishing post-production the project went through three different producers.
There exists one voiceover directed by Ridley Scott of dialog written by David Peebles (who wrote most of the draft of BR that was shot, as well as Unforgiven). The first new producer hated it and. There exists one voiceover that the producer liked, dialog written by a guy who didn't like sci fi and was basically a buddy of the producer. It tested really badly, Ridley Scott hated it, and eventually the producer bailed. Then a second producer came on board and wanted a whole 'nuther try. Ridley Scott and Harrison Ford, sick of all this bullshit, did their take really badly to force the production into using their original voiceover (or going with no voiceover at all, a direction Ridley Scott was favoring). They tested it without voiceover and didn't like the results, so they tested it with the awful voiceover and it was less terrible, and they rushed the film out because holy shit it was bleeding cash.
It's easy to point the finger at bad producers with no vision. It's hard to remember that The Ladd Company nearly went bankrupt Bladerunner was so expensive. It was in theaters next to E.T. and cost a lot more. Blade Runner was the most expensive film released in 1982 and if they didn't get it out it would have been a total accounting loss.