don't have a answer but a question. you said you have table mates. we've not been a cruise yet, but do you always have someone at your table, even at anytime dining?
The smallest tables are for two, so it's normal to have someone at your table. Of course, the "someone" may be your wife....
If you book "Traditional Dining," you can request a table for two, four, six, eight, or ten, depending upon the ship. The Maitre d' will attempt to accommodate your request, but there's no guarantee that he (or she) will be able to do so.
If you have "Anytime Dining," you can request to be seated alone or to be seated with other passengers. If you request to be seated alone, you may have to wait until a small table becomes available.
But meeting other passengers and making new friends is part of the fun of cruising. I would not dream of asking for a small table!