The crowd gasped with oohs and aahs when Chris Sheldon pulled his company’s new gadget from a silky black bag in front of hundreds of techies.

“We are very proud to introduce the least-advanced NoPhone ever,” he said at a technology conference in Canada this month. The NoPhone is a plastic rectangle that looks like a smartphone but does absolutely nothing. More than 10,000 have been sold in the past two years for about $10 each.

The...