alt Hacker NewsOr on purpose, because the CPUs with AVX are more expensive. Or historical: the hardware for this kind of service may have been old, and you can't tell people that if you buy today you get a processor with AVX, but tomorrow you may get one without. I haven't checked if they upgraded their low-cost options in a while.
You can try to execute POPCNT. If it does not fault, its presence is only hidden via CPUID.
Live migration support may be the reason why they stick to the baseline. That's most likely to be migratable across different CPU types. Although with a bit of effort, you can figure out what is support by your fleet and configure that into the hypervisors.
I'm skeptical that pre-SSE-4.2 etc. CPUs are economically viable for running customer workloads due to electricity costs.