Benefits of migrating to Azure
Typical Linux deployments in on-premises environments are based on VMs, and migrating them to Azure falls into the realm of IaaS, so they will still be VMs after the migration. For sysadmins, this means the same skills they already have and the same familiar management tools are still useful on Azure.
In the early days of Azure, some services were not designed for Linux use, and users sometimes got frustrated by the complexity of using Linux on Azure. Being originally named Microsoft Azure gives a hint as to what use cases it was designed for. Since then, Azure has evolved and it has been developed to be more and more Linux-friendly.
Note
Linux has rapidly gained popularity in Azure. In 2015, Mark Russinovich, the CTO of Azure, said that one in four VM instances in Azure runs Linux. In 2018, Microsoft Cloud EVP Scott Guthrie revealed in an interview by ZDnet that about half of Azure VMs run Linux.