The "All you need is NAT" argument is correct to a point.
Most infections/attacks are "Pull" not "Push" these days, because most networks have NAT.
Piggy backing on a NAT connection is, to my knowledge not something "typically" done. Not in the "Who can I infect?" automated sense anyway.
If a router exists with a vul, it will be in scanners already which will be looking for that signature and reporting it back to their master.
To make it even "sane" you need a "Personal firewall" on the windows PC. That is a firewall which watches your application/process connections and allows/denies OUTBOUND connections on a port per port, application by application.
A standard way to bypass firewalls is to run an agent on the host which connects out to you, rather than the other way. Consider FTP. Vanilia FTP the client connects to the FTP server "Command channel" and the FTP server connects back to the client for a data connection. This does not traverse NAT. So "No Passive" mode was introduced so that the client now starts the command connection and when the remote is ready, the data connection is also outbound. Opened "on behalf of the remote", if you will.
Modern infestations, infections and attacks use the same technique. How do they get the agents on your PC? Usually web browsing and email. "Usually".
It's often not a one step process either. Sometimes the initial attack does nothing but install a helper. That help then starts 'reaching' out to the internet to inform "its masters" of where it is, request instructions. Basically a backdoor. There are websites you can got to, if you are brave, which provide realtime updated lists of identified vuls with meta data and IP address. There are better ones, but you have to pay bitcoin for them.
Then we come to the "network neighbourhood". The IP space around the machine in question. Once inside your NAT they (automated scanners or a real person using the backdoor) will have free unabridged access to everything on your LAN. That means that your messy, not updated Windows 10 machine that you got infected browsing pron, is more than capable of finding your firewall-less, antivirus less Windows 7 machine or VM and infecting it.
80% of the security in corporate sectors is internal. Preventing one infected computer from infecting more computers is where the smarter companies with money to spend on security put it.