Can fans convince a streaming site to show a certain anime? If a streaming site, for whatever reason, doesn't have a certain anime of which you're a fan, can you gather enough votes in online petitions or facebook likes to convince the site to start streaming it?
When could this work, and when would this be hopeless? For example: do studios decide not to work with specific streaming sites, regions or audiences of less than N viewers?
In most cases: No. They don't care about the fans, and care about profits. Most streaming sites have licenses to stream that show, which often enough is for exclusivity, such as with Netflix, or Amazon Prime. The licenses for these shows are either expensive from competition for it, or not worth the cost because of lack of response for the series. In the former case, the streaming site you're petitioning can do nothing about it, considering some other place will most likely already have the license, and in the latter case, can't see enough profits coming from it to make it worth the cost.