"You can now reserve public IP addresses and use them as virtual IP (VIP) addresses for your applications. Reserve up to five addresses per subscription at no additional cost and assign them to the Azure Cloud Services of your choice. In addition, you can now assign public IP addresses to your virtual machines, so they become directly addressable without having to map an endpoint to access them directly."
When Azure IaaS was first introduced, you could not ensure that public facing IP address of your VM or cloud service would remain the same, particularly if you shut down all the machines within a cloud service. What Azure would retain for you was the DNS name you created within the cloudapp.net domain. The recommended practice was to use DNS to locate your services, instead of relying on a specific IP address.
I know, we all love the comfort of knowing our IP address. Over the past decade or so, I lovingly handed out the easiest internal and external addresses we had to servers I accessed frequently. Stable IP addressing was a must - changes often meant re-configuring firewalls, routers and even some applications, which could lead to downtime and complaints. Even Azure's long term lease for IP addresses if your cloud service was active, wasn't comforting enough for many who had been burned the past by a hard-coded application or some other IP address nightmare.
But it's not 1998 anymore. The Internet isn't a quaint little place you go to read text and your "mobile" phone isn't hard wired into your car. IPv4 addresses are exhausted at the top levels, it's just a matter of time before your internet service provider won't have anything to give you when you ask. For a while I firmly believed that IANA would open up that special "Class E" space to buy extra time, but nope, it didn't happen.
So yes, if you have a legitimate business need to have reserved public IPs you can go reserve some public IP addresses in Azure to meet your needs. The first five are free if you are actively using them. But think hard about what your business needs are. Do you have an application that needs a static public IP address? Maybe it's time address that requirement within the application itself. Do you update applications by swapping IP addresses? Maybe you should look more closely at the options within Azure to swap staging and production deployments.
But if you aren't thinking about IPv6 and just want to try to buy some time in the IPv4 world, you might want pause before hunting down the necessary PowerShell to get that done. This is why name services existing in the first place - so you don't have to learn and remember IP addresses and don't need to latch onto them for all time. Once IPv6 is fully deployed across all the major players (cloud providers, ISPs, etc) you won't even bother trying to remember a 128-bit address. Unless you are trying to impress people at bars.
No, I'm pretty sure there are better ways to impress people at bars.
So don't bother with hoarding up IPv4 addresses, just embrace FQDNs, DNS, and start preparing for IPv6 so that when it comes to you, you'll be ready. In the great words of my preschooler as she dances around singing Disney songs, "Let It Go". FQDNs are the future and the exhaustion of the IPv4 address space will make that so.