Of course, in a couple years, assuming success, the AWS lockin will suck. But given the odds of success I think I'd take the chance.
Otherwise let AWS grow the market, and look for opportunities to serve people who don't want to pay the AWS premium and/or to plug feature holes.
My biggest complaint about MS/Azure is they can't seem to get single signon/off working right... Login to one account for personal email, another for work email, and another still for my personal Azure account... Sometimes gets stuck in a loop, just doesn't work, whatever... I often keep another browser, that I don't mind wiping all cookies on just to get the damned thing to work. Let alone the other day where my payment didn't go through for some reason, and my azure account was locked, as was my live account, that I had to go through a convoluted recovery process that was different because of 2fa, only then to have my email (application password) revoked... grrr.
Despite account issues, I've really liked actually working with Azure.. though I think their node tooling could use some TLC, and better documentation... wound up writing my own wrapper (azure-storage-simple) to have a cleaner interface... also wrote mssql-ng as a friendly abstraction on top of mssql.
Is Tyk HIPAA compliant? I'd definitely like to use something like Tyk, but I manage an API that transmits health data, so lots of tools have turned out to be off-limits because of HIPAA issues.
However, we'd probably need to do an audit. Worth a check though.
We've been considering building something like this ourselves or looking for a good existing solution, but hadn't found anything yet. I'm definitely checking this out.
Flexibility however is always something you run into with platforms. And while this is a bit different then what folks typically think of as a platform (Django, Rails, Play, Spring) it looks like it would suffer the same problems. As soon as you need to do something weird, you're stuck fighting the platform or porting out instead of making your project better. This is why I prefer platforms that are more a collection of libraries with a preferred way of doing then as opposed to rigid box box style things.
We are accepting pull-requests from the community for new Plugins (http://getkong.org/plugins), and I can see Kong running on top of the AWS Gateway -> Lambda integration to provide functionality that is not necessarily bound to the AWS realm.