Hyper-converged infrastructure benefits are well documented: HCI is easy to set up and run, and it's software-defined so you can change it as needed. But HCI has downsides, too.
For example, to scale up, you have to add another whole node. This means more storage, compute and networking resources when you may only need to increase one of those. Right-sizing your HCI is critical, but it's not easy. To that end, some organizations choose converged infrastructure instead; CI allows you to snap on more storage or compute nodes without scaling the whole cluster.
Vendor lock-in can also be an issue with hyper-converged infrastructure. One benefit of buying an HCI appliance from a vendor is tight integration of the hardware through virtualization, but it can limit you in terms of which other systems your HCI can integrate with.
As an alternative, you could use any hardware you want -- maybe even hardware you already have on hand -- and purchase hyper-convergence software from a vendor. This kind of DIY HCI provides the integration companies interested in hyper-converged infrastructure benefits are after, but it comes with more risk than using hardware and software that a vendor has certified to work together. Depending on how you assemble your DIY system, you might not get the troubleshooting support you need when something goes wrong.
When deciding between HCI, CI or another data center infrastructure, the use is paramount, but there are still pitfalls for each configuration. For example, high-density data centers can easily reap hyper-converged infrastructure benefits, but they also face different issues than smaller server footprints. HCI vendors offer solutions to power and cooling problems for high-density situations, but they might not be so helpful with figures about how many VMs and containers their HCI can support.