I would have thought the only benefit is that your IP never changes so you can always get to the service/server no matter what.
We use static IPs at work for various reason.
1. We know what site is talking to us always as only trusted IP's comes though the firewall.
2. We have a static IP range and only our IP range can connect to each router on site making it more secure.
3. We can access any device directly as each site has up to 6 IP addressed devices
4. with 250+ routers you don't want to be setting up DNS services on each one!
Normally your IP gives you an IP that changes, meaning if you run a PC at home you would find it hard to connect to while out as its address keeps changing; unless you use a dynamic dns program that updates your IP when your ISP changes it. In reality ISP like Blueyonder/Virgin don't tend to change your IP often but if they wanted to they could, as for others I'm not sure how often they change
The question is what do you need one for?
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