The only scenario where I see disabling downvotes as a good idea is when upvotes are disabled as well.

So you either:

• have only number of views (no up/down votes) so people don't chase virtual points
• or there are both of them so that when combined they result in a fair rating.

Upvoting without downvoting doesn't show if people like it, nor whether it is good or bad. It only shows that it reached a lot of people and is popular. And that can be achieved with views alone.