Yes, this is a big issue for many infrastructure startups. The AGPL scares potential users and customers away, but permissive license often get taken advantage of.
At FOSSA, we've commissioned a new license called the Commons Clause (http://commonsclause.com/) that tries to address this exact problem, so that developers can create permissive software without being exploited by providers.
What's the point of using a permissive license then? Why not just use a (situation appropriate -- i.e. LGPL, GPL, or AGPL depending on what precisely the software is) copyleft license?
The point is to prevent service providers like Amazon from making money by the software you built, but still allow end users to operate and self-host and modify it.
I've recently seen http://scip.zib.de/#license. " You are allowed to retrieve SCIP for research purposes as a member of a non-commercial and academic institution.". Could help keeping alive an academic community around it.
At FOSSA, we've commissioned a new license called the Commons Clause (http://commonsclause.com/) that tries to address this exact problem, so that developers can create permissive software without being exploited by providers.