I answered a similar question a while back, here. Azure has evolved since then:
Azure's AppFabric Cache is currently in CTP (community technology preview) and will go live some time later this year (sorry, I can't quote a date). With a single configuration change, you'll be able to enable the asp.net session state provider without changing any code, and have your session state available to all of your web role instances.
With Azure v1.3 which rolled out in November, you have have the ability to run tasks at startup with elevated privileges (e.g. to run an MSI to install some prerequisite control suite).
For monitoring, you can take advantage of Microsoft System Center, which now supports Azure directly. Alternatively, you can look into 3rd-party options such as AzureWatch.
With Azure's extra-small instance, you can run a site for approx. $44 monthly. You mentioned catastrophic failures and SLA. With Azure, you need a minimum of two instances for SLA to take effect (this is because your virtual machines are located in physically different areas of the data center, in separate fault domains). So you're looking at approx. $90 / month to run a site with 99.95% uptime. Only you can determine whether this is worth it to you. Yes, you can host with a simple hosting provider for significantly less (such as GoDaddy). However, if your site fails there, you have to wait for it to be detected and then installed on a separate box. Also, you share each server with potentially dozens of other tenants, which will impact your site's performance. With Azure, at most 8 tenants will occupy a box, depending on how many cores you configure your virtual machines to use. And it's incredibly simple to scale up or down to handle traffic increases and decreases.