I have been in cafes/coffee shops alone, and have had people ask me if they can sit at my table - as there are no others free, and I say 'of course...' Because I am not entitled, and self centred, and so precious that I think I own the fucking table and no-one is 'allowed' to sit with me.
And, I have never EVER had the person/people trying to engage in conversation with me, because if they're alone, they're alone for the same reason as me - because they want half an hour to themselves to have a coffee and a read through their phone/read of a magazine. (And if they're with someone else, they want to chat to them.) These other people are NOT interested in having a conversation with a stranger, no matter how important and special that 'stranger' thinks they are. 
If someone is so precious and fragile that they can't bear someone in a public place speaking to them, (or GASP wanting to sit 2-3 feet away from them,) then I don't understand why they even go into a cafe alone. I am willing to bet that the amount of people trying to get them to chat is vanishingly small - if any at all. It never happens to me. Other than 'can I sit here please, I can't find another seat' the person/people says nothing else. As I said, other people don't want to chat either.
It is breathtakingly entitled and rude to say no to someone who wants to sit down when there is a seat at the table you're sitting at (and there is nowhere else to sit.) It's not YOUR table, you don't OWN it, and you have no right to dominate it. How rude!
If there was a seat (or more than one) available at a table, and that was the only table with free seats, and someone said I can't sit there, (when I asked politely) I would tell the staff. I am sure they would put them in their place, and tell them they don't own the table!
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