But isn't dedicated providers a subset of cloud providers? I can see how having a focused provider with a narrow mission might be beneficial in some cases, but I can't say it's that much of an advantage compared to the ecosystem & convenience of a cloud provider.

what's an example of a dedicated provider?

I also worked in ITOps at a medium-ish company and we were moving our colo to Azure, when I left.

There are thousands (tens of thousands?). OVH is probably the biggest by server count. Softlayer arguably had the most potential (prior to its IBM acquisition). Hivelocity, ReliableSite, WebNX, Hetzner, LeaseWeb, Online.net, DataPacket, QuadraNet, PhoenixNap, ...

Hetzner, scaleway and packet.net come to mind

i3d.net will give you a machine, with as hands-on support as you want up to even patching the OS.

Rackspace

The guys that are selling managed services on AWS?

They sell all of those those things. RS has their fingers in many pies, even though some of them appear to conflict at first glance.