There are several reasons why a move from on-premise machines to Azure Infrastructure as a Service (IaaS) makes sense. This article on TechNet describes top reasons why BizTalk servers could (and could not) be moved. A series of scenarios are presented, with their respective recommendations. Note that there are some differences based on the BizTalk Server version. The upcoming 2016 version has added support for High Availability (and more) in Azure.
As the article describes, there are several factors that need to be considered before making the move to Azure. Although there are many compelling reasons for moving, it is important to take the possible showstoppers into account. The main takeaway is to take all known factors into consideration, and make the best decision possible for the business.
Update! This article was recently awarded BizTalk Technical Guru Silver Award for September 2016 on TechNet.