Interesting. The heirloom magic erasing sword can't actually be used as a sword. It's basically a magic tool in the shape of a sword, but as a sword it's just decoration. Maybe it would instantly shatter if Ex tried to hit anything with it. If this was some other series, I'd criticise the author for not pointing that out earlier, but since this story is 99% of Ex professing his love to Alice or Ex lamenting how he can't spend 24/7 in Alice's company, it can't be helped. A panel used to explain the sword's weakness would be a panel away from Ex praising Alice to anyone (un)willing to listen.