If the government forced Twitter to ban the account that could set a bad precedent. A right-wing demagogue could convince people that a reasonable, non-violent left-wing group (or even a centrist group depending on how extreme the demagogue is) is a threat and then force Twitter to ban it, ditto for if it's a left-wing demagogue. No matter how worthy something seems of censorship censoring it opens the door to censoring things less worthy of censorship.
That being said Twitter is a private company and has the right to ban whoever they want, and I think they should make the decision to ban the ISIS account.
Hate speech and terrorism should never be tolerated and allowed to continue on social media networks, including Twitter. While private companies can determine their individual policies for use, in today's world there are few corners of the earth where the message of these morally reprehensible people would have a venue to publish their voice. A company that operates in the free world should be able to uphold the difference between free speech and hate speech.
ISIS poses a serious threat to the World and must be defeated. This means shutting down their ability to spread propaganda and recruit new members online. Social media sites like Twitter should not be used to support any violent group that seeks to kill innocent people. Twitter shareholders should demand that their company will not be used as a way to promote this terrorist group.
It is my opinion that Twitter should not ban the account of ISIS from its server. We are not discussing anything that would give ISIS valuable information that could be used for harm. Rather we are giving ourselves insight into the twisted minds of those that post on the ISIS account.
ISIS should not be banned from having a Twitter account. This is a way for investigators to keep track of the group and the message they are trying to spread. Although the extremist group uses social media to its advantage to recruit members and spread propaganda, governments can also use it to their advantage.