If there is burning it's from acid not lack of it.
Acid suppressant drugs produce a state of hypochlorhydria intentionally so it is important to prescribe just sufficient to manage.
Acid in the stomach will start to dissolve out the essential elements from the food to be absorbed in the duodenum and intestinal tract. Some material does not break up with acid requiring the bile that is normally released into the duodenum by the gall bladder.
In some cases, bile is permitted to reflux from the duodenum into the stomach back through the pyloric sphincter to assist in the breaking down of that material (e.g. meat) before it reaches the duodenum.
If that acid and bile refluxes into the esophagus, firstly the acid will scour the mucus away and burn the lining of the esophagus inflaming it - heartburn and esophagitis. Then the bile can start to work breaking down the flesh of the esophagus itself.
To defend itself the cells that line the esophagus will change: columnar cells which present a smaller face to the bile. This is what we call Barrett's Esophagus. It is a permanent change which may progress to cancer of the esophagus.
But to produce Barrett's Esophagus, both bile and acid are needed. If it's not possible to stop the reflux, we must stop the acid and/or bile. Acid suppressant medication stops the acid. Q.E.D.