Mainframes are more efficient at some tasks. Most tasks aren't particularly suited for mainframes, but the ones that are become a lot more expensive if you try to put stuff into the cloud.
You're also often dealing with very sensitive information. Zenbleed style attacks are an unacceptable risk, so you'll need separate hardware from the rest of the cloud anyway. Maybe you can find a data center that's reliable and secure enough to put all of that sensitive data, but there's a good chance you'll be wiring up your basement with fiber optics if you're dealing with finance.
The cloud, as in "other people's computers", is horrifically expensive. If you're going to set up mass throughput systems, you'd better start your own data center. This is expensive as well, but it's not impossible.
If you want scalability to reduce power consumption and deal with burst workloads, you'll have to separate out your processing systems from your storage systems. Your average data center probably runs a lot of iSCSI or similar remote disk tech, possibly based on some kind of software wrapper at the cost of latency and performance but with the benefit of quickly swapping drives and expanding capacity.
Then you'll have to architect your software, of course; if you're doing batch work, you'll probably want to distribute programs in batches and run similar programs on similar chips, making optimal use of data locality and CPU cache. Maybe do the whole Hadoop thing depending on your workload.
You'll also want to figure out maintenance. You can hire a team of your own techs dealing with replacements or upgrades, but in many cases hiring external talent for a limited amount of time per month is probably cheaper and saves you the effort of keeping your workers trained.
When a machine fails and the SKU you've selected has gone out of production you'll need to figure out a replacement. This doesn't have to be a problem, but servers are fickle things and you'll probably want to use something that works with the other server vendors' tools, so you're stuck buying hardware from a limited number of suppliers in a limited number of configurations.
For management, you'll want to pretend all the computers are part of the same system. Whether you pick Kubernetes or OpenStack, you want central control to save you the headache of a million dashboards.
When you're done, you've built yourself a mainframe, except you've spent your own money on R&D and need to spend money to upgrade your hardware rather than buying licenses for the rented machines your mainframe vendor already shipped to you, waiting to be licensed. Have you saved money compared to buying overpriced mainframe hardware? Tough to say, mainframe hardware is often better at its job than normal servers. You'll save money on developers, as you no longer need to keep the old COBOL around, but when that happens you've probably paid more than you've saved when the decade long project to rewrite the backend to another language is finally done.
Mainframes are just computers good at batch jobs. They're not better or worse than regular computers, they're just different.