Sure you need net/infra admins but the software and hardware these days are pretty management friendly and you'll find you still need (often more expensive "cloud") admins so you're not offsetting much management cost there.
Colocation is plentiful and providers often aggregate and resell bandwidth from their preferred carriers.
At one point we were up to 8 dell vrtx clusters and a few SANs, with 500+ VMs from huge msSQL servers to kube clusters the public cloud bill would have been well into the 6 figures even with preferred pricing and reserved instances. Our colocation bill was $2400/mo and that was mostly for power. The one thing that always surprised me was how much faster everything was - every time we had to scale-over into the cloud the public cloud node was noticably slower even for identical CPU generations and vcpu.
You need to be very keen about server deals, updates, support contracts and licenses - but it's really manageable and interconnecting with the cloud is trivial at this point - you can get a "cloud connect" fiber drop to your preferred cloud provider and connect your colo infra to your vpc.