The only negative, in my opinion, is aesthetic. Exposed, open plants looks more attractive to me than beds with low tunnels over them. Still, exposed, open plants look more attractive to pests like leaf miners, too, apparently. I can't really blame them. For me, its well worth it to sacrifice a little in the way of aesthetics in the interest of not having to deal with leafminers anymore. Also, I suppose they may not work well with crops that need to be pollinated by flying insects. I am not certain about that from my experience as most of it has been with leafy greens and other non-flowering veg.
After the success with the leafy greens the first year we started using the low tunnels over additional crops in the following year. Cabbage is another vegetable that frequently attracts unwanted insect pests and the covering works well at discouraging cabbage moths, too.
They don't hold up to hail, we have learned. Oh well, nothing last forever...
We'd totally recommend low tunnels of row cover for pest prevention.