With a cloud it also means that when there is an outage there are potentially many sites/services affected all at once, and there is potentially nothing customers can do to fix it other than wait (or plan in advance, and use/pay for multi-AZ/multi-region/multi-provider redundancy).
Such outages are also possible with traditional hosting providers, and when an outage does happen I'm not convinced whether a large public cloud would recover more quickly (due to better resourcing/expertise available to fix the problem), or a small hosting provider (which may have a smaller team, but the problems they deal with are at a smaller scale and more easily fixable).
Either way you probably want some kind of CDN independent of your cloud/hosting provider that can help survive some of these glitches.