Once you have scaled to beyond the performance available on a standard setup on a single box without preparing to scale out, you face increasing costs in a migration because you potentially have to re-engineer your app to be able to run on a very different stack.
Compatibility at the connection level is just one part of a whole lot of issues to take into account when considering whether or not you can migrate elsewhere easily.
Given how expensive AWS is, that's something to seriously consider.
Well if only AWS provides the scaling you need then what would you migrate off of AWS to? You could re-arch your app to scale out for some use cases as you suggest, but that's also an indicator that using AWS allowed you to get to market faster with a much simpler system that didn't require a far more complex design, many more engineering hours and more admin.