You can also simply spend some coins over the Lightning Network if you don't want to pay the swap fee. You will gain incoming capacity this way.
As far as I've understood this happens so the node that you're connected be able to know how many bitcoins there are left to be received (from your channel)
I am not sure what you mean by that. In short, when you open a channel, you cannot receive any coins through it because the other person does not have any coins on their side of the exactly same channel. As you spend coins through that channel, the balance of the other party increases. Once their balance is higher than the required channel reserve, you can receive coins through that channel.