nigelivey :
jsmithepa :
As in all answer to this type, IT DEPENDS. There is no fast answer unless you provide more detailed into like modem or gateway? ethernet router or wifi router? which box is currently doing DHCP (somebody must do this job and if the modem can't then who's going do it when you remove the router?) blah-blah-blah.
Lastly unless it bothers you in some way, leave well the dog lay. It's working, don't try to fix it.
DHCP isnt strictly necessary is it.
The ISP gives you one IP address, to the modem.
The modem gives up one IP address, the same.
If the single PC is connected directly to the modem, the PC gets that public IP address.
If there were a router int he chain, that public IP only goes to the router. After that, devices get internal IP addresses, not directly routable to the outside world.
Let's assume the ISP gives you an address of 72.145.250.101
A typical port scan from outside would go to that IP.
Modem -> PC means that port scan is directly to the PC.
Modem -> router -> PC means the port scan goes to the router (and its firewall), not to the PC.