Since this question is from a user's (developer's) perspective I figured it might fit better here than on Server Fault.
I'd like an ASP.NET hosting that meets the following criteria:
I researched but there seems not to be such a platform, that completely abstracts the underlying architecture away and thus has the ease of use of a simple shared hosting but "unlimited" scalability.
"Single server" and "scalability" are mutually exclusive, I'm afraid. But a good load-balancer will apply affinity to requests so you don't need to needlessly double-cache data on multiple servers.
However, well-designed web applications are easy to port to a multiple-server scenario.
I think your best option is something like Windows Azure Websites (separate from Azure Web Workers) which run on a VM you don't have access to. The VM itself provides enough power as-is necessary to run your website, so you don't need to worry about allocating extra CPU power or RAM.
Things like SQL Server are handled separately, but is very cheap to run, and you can drag a slider to give yourself more storage space.