It is absolutely possible to do that. I work for a university that was lucky enough to get a Class B network (a /16 network in CIDR notation) back when they were passing them out (very roughly 20-25 years ago). Right this very moment my workstation, a workstation mind, is parked on a publicly routeable IP address. In fact, we have relatively few RFC1918 addresses in use. The few that are in use are used for PCI compliance (the standards mandate NAT) and network management. You just can't GET to my workstation from the public internet because the firewall prevents access.
In fact, the machines in our innermost secure sanctum are also running on public IP addresses. There are two firewalls between them and the public internet. When we contract for 'security scans' from 3rd parties, we have the ability to give them unrestricted access from an IP address they specify, which gives them the next best thing to 'on the same network' scanning. And then we take it away from them, and they can't get back in. It works great. Heck, this is how the Internet was intended to work back in that more trusting time before spam was invented. It still can.
In fact, IPv6 was originally designed around eliminating the need for NAT. There will be enough addresses for everyone, so the need to hide behind such gateways was (in theory anyway) made redundant. In other words, make the Internet work the way it was supposed to work. NAT support was bolted on very late in the process, in no small part due to staunch advocacy from the part of the InfoSec establishment that values invisibility as a defensive measure.
The key thing to keep in mind here is that NAT is not a fundamental function of a firewall, it is merely closely associated. When used with a firewall it merely obscures what attack surfaces may exist behind it. Our internet-facing firewall isn't doing any NAT at all, and our intranet-facing firewall is only doing a little (PCI-related).
I know many, many computer professionals who get a shiver when they discover the IP address of their device is publicly routeable. It is no less secure than an RFC1918 address when behind properly configured perimeter security devices. This 'public IP is bad' concept is enshrined in the PCI standards, and will have to be reassessed in light of wider IPv6 deployments.