EVERYTHING has recognizably distinct properties.
No, objects having recognizably distinct properties does not come for free. You are probably missing that I'm describing objects, and that I use the term "recognizably".
Suppose we have 10 glasses of water. I take 3 of those glasses and define it as "foo water". But I don't tell you which 3 glasses are foo water.
Your task is to pick out which 3 glasses are foo water, versus which 7 are not foo water.
Compare that to this situation. We have something I call a carpet, and something I call a television, in a room. We shut the room, soundproof it, surround it with a Faraday cage, and so on, and I just rearrange the room to my heart's content. Then we open the room and let another person in. Her task is to identify which one is the carpet, and which one is the television.
Do you understand?
What you have to say is why you chose THESE particular properties. The properties themselves don't choose themselves for you.
No. I do not have to say why I chose those particular properties. Why I chose a particular set of properties is entirely irrelevant; if there even are particular properties that are different for the television than there are for the carpet, then it follows that a television is not the same as the carpet.
The fact that we can perform experiments such as the second one I listed above, and have a person correctly identify the carpet and the television in nearly 100% of the cases, means that there are recognizably distinct properties, which necessarily means there are distinct properties.