I've done large colo deployments. When you're provisioning your own hardware it's cloud-init, ansible, K8s, whatever. Nothing even knows you're in colos operated by different providers in different regions. Nothing knows or cares you're using five different upstream internet providers (whether your own - complicated or IP blends from the colo).
Have a falling out or big issue? No reputable colo provider is going to hold your hardware hostage (it's the physical world and legal and reputational issues heat up quickly). They'll be happy to ship it out (get rid of you) to another provider, who will be even happier to re-rack. Meanwhile if your architecture is even remotely well designed (load balancer, multiple facilities) you're never down and it's not even that much of a "fire drill". With the capabilities of modern hardware this is often a single 1U redundant HW machine.
All of this, by the way, is a fraction of the cost of cloud solution (a $25k bonkers 1U is ~$700 a month with a three year lease and 1U hosting + bandwidth + power is ~$200 a month). So for $2k a month (and it's actually predictable) you're up in two facilities and have capabilities an order of magnitude greater than a big cloud at equivalent spend.
Companies screaming on twitter and profusely apologizing to their customers due to the most recent "name a cloud" outage demonstrate that multi-cloud (and even multi-region) is extremely difficult if not impossible to do in practice.