How "cheap" it is not to order drinks together with the meal in the restaurant?

I'm perfectly aware that restaurants generally make money on drinks,

Restaurants make plenty of money on meals. Not ordering drinks or just staying with tap water (depending on country) is perfectly fine.

Many people don't drink alcohol and non-alcoholic drinks are often inexpensive and not something many restaurants care too much about, especially if they offer free refills.

It is perfectly fine. You do not even have to order an entire meal. Most restaurants will let people order just an appetizer, or desert, etc. Only once in traveling to 63 countries did I encounter a minimum order and that was in a very popular New York restaurant. We did not have to order drinks even just that the per-person order was above a minimum.

You are correct that drinks are a high source of income for restaurants since the cost-to-price ratio is higher on drinks than most other items and most drinks do not require much preparation, so cost little in labor but there are plenty of items that vary greatly in how much profit a restaurant makes on the item. Don't worry about not maximizing profit of the restaurant!

In several countries of the world you can order water at no cost, particularly where tap-water is safe. If it is not, then you will be charged for water. Then you need to watch price because I have seen places where the charge for beer was less than for water!

There are other local customs when you get served a drink without cost. For example, Chinese restaurants often bring tea as soon as you sit down before you order anything. They constantly make more tea and the cost-per-teapot is low, so this is complementary and you will not be charged for it later when the bill comes.

Be careful with other items appearing on your table before ordering though as in some unscrupulous tourist traps, this is a common tactic to inflate you bill. Always ask as soon as something appears so that you can refuse it and avoid a charge later.

In some places, the opposite is true. I never needed to buy water - even bottled - in Taiwan because almost every place gave out at least one water without charge. This happened on buses, gaz stations, hotels and even museums! Many times even cookies came along! They always specified is was a gift, probably due to my puzzled look!

when the money was more limited, and I needed to eat something when travelling, I used to save costs by drinking my own water before entering the restaurant and order meal only.

No need to do that in France: restaurants must serve water for free to their customers, as required by law (mirror 1, mirror 2). Not paying for water isn't seen as cheap, but typical.