Sorry can't see the logic in wanting to sit alone, cruising is about mixing and meeting people, we have met some lovely people on ships, but if you want to sit alone just request a table for two when booking, and you will be catered for.
Both P&O and Royal Caribbean ask what size of table you would like be on when you book your cruise eg 2,4,8 or 10, so you will be able to request a table size to fit your party. It can't always be guaranteed, but we have never had a problem so far.
Do not fret, Oceana with P&O offer freedom dining, eat when you want and with whom you want, even a table for two if you fancy it. RCL and also Island cruises offer this. With companies such as RCI, even though it is a fixed dinner seating on their ships you can always choose to eat in other restaurants such as self service or premium eateries on board so you never have to eat with people on a fixed seating if you dont want to.
We asked for a table for 2 as it was our honeymoon & they put us on a table for 12!!! We requested a change & this was done in time for the 2nd night of dining.