A few IPs are reserved for broadcast and network purposes.
Using a router is a better idea--for the very reason you discovered. Having your very own provider-assigned IP address exposes each machine to the dirty dirty nastiness of the Internet, requiring per-machine firewalling. Using a router with NAT blocks most of those things. And most NAT routers allow port forwarding and other ways of exposing only the services you want to the world at large.
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