I'd agree that freezing means that they might come back. Verrucae are caused by a virus - if you cut them out, then you may not have generated enough antibodies to be immune to them in future.
I had a whole patch of verrucas for years on the ball of my feet. They never bothered me until they started to have another spurt and started spreading to the side of my foot. I then started on the salicylic acid route which was extremely painful (as it was such a large area - a chiropodist had refused to cut them out). I had to stop as I was going away skiing, but by then I only had about a few left (including thr Mummy and Daddy ones - the original two).
What was interesting was that once I got back, I noticed that they were disappearing anyway - it was like I got the infection down to a manageable enough level that my body could get rid of the rest.
That's maybe why the "gentler" remedies, like the essential oils, work, as they are working in harmony with the body.