For the others of us whom have 'real lives' and 'other things to do', copying off the useful stuff and reinstalling /re imaging/reformatting IS the best and most intelligent course of action.
And in the long run almost as time consuming as repairing the damage instead. Having to retrieve everything you want and restablishing the appearance and set up which the user likes and is used to also takes time. It does of course assume that the users data is all neatly stored in sensible places and easily transferred to an interim medium or backed up even. In my experience that is rarely the case. Hence the user loses all sorts of stuff but hey, who cares, you can get on with your 'real life'.
Besides. Some may install a rootkit which is virtually undetectable.
Rootkits are perfectly detectable and removable. They are also becoming more common.
You can EASILY become infected behind a router or firewall if you access the net at all.
Of course you can but then the fundamental purpose of a firewall is not to prevent a virus infection.
G String
You will be able to boot into safe mode. The initial actions to remove malware can be a little difficult and slow because the malware itself often obstructs attempts to remove it and also blocks access to helpful internet sites if not all internet access.
Do you have access to another PC? If so one useful technique is to download the programs you need to a USB memory stick and run them from there. You sometimes have to rename the programs you wish to use to prevent the malware recognising the program you are trying to run.