You are doing the polite thing. When I used to travel a lot for business, I was never without a book to keep me company.
I finally got brave enough to ask the maitre d' in a nice hotel restaurant if there were another person dining alone who might like company. I met some wonderful people that way.
What the complaint is here that people who are NOT eating, drinking, etc. are hogging tables for people who want to EAT and can't find a place to sit because there are no empty tables.
Of course, this could be remedied by going to the main dining room.