I'm no expert and struggle a lot with swarming myself, but I think for the most part the kind of "space" they care about is space for the queen to lay. Secondary is space near the brood area, especially just above it, where they feel they need to have honey stored before they can swarm. Physical space for the bees is far less important.
Maybe it could be a slight issue if a huge colony was compressed into a single deep, but I don't think a single queen can produce more bees than can fit in 3 deeps, so I don't think removing capped honey supers above that 3rd box would have any effect.
When you see them bearding that's usually more about temperature regulation than physically running out of space, I think.
Look at Ian Steppler's videos. By this time of year he's reduced huge stacks of deeps down to a single deep, causing tons of bearding, and from what I can tell very little swarming. See here for example. He has more of an issue with swarming during the early flow. But I don't know, your climate and bees and management are probably different.
Maybe it could be a slight issue if a huge colony was compressed into a single deep, but I don't think a single queen can produce more bees than can fit in 3 deeps, so I don't think removing capped honey supers above that 3rd box would have any effect.
When you see them bearding that's usually more about temperature regulation than physically running out of space, I think.
Look at Ian Steppler's videos. By this time of year he's reduced huge stacks of deeps down to a single deep, causing tons of bearding, and from what I can tell very little swarming. See here for example. He has more of an issue with swarming during the early flow. But I don't know, your climate and bees and management are probably different.
