Some kind of physical record of a vote is necessary in case of technical problem with electronic voting machines. Hackers could compromise the software of an electric voting machine, or there could be a power outage that prevents votes from being recorded on election night. There should be a backup system of recording votes.
Voting done purely via electronic devices can be too easily tampered with. Something may go wrong with the machines, the information may become corrupted, or someone may find a way to hack the system and change the results. However, if there is a paper trail, it will be much harder for anyone who wants to alter the results to do so. Plus, if something goes wrong with the system, there will be back up records to consult about the voting results. So yes, electronic voting machiens should have coter verified paper audit trails.