Question about pH and HCl in the stomach

Have to get the H+ from somewhere and that would be HCl.

That would make sense, but apparently the H+ is secreted from an entirely different channel. From what I understand, the chlorine exits by following potassium and sodium, and it later binds with H+ inside the stomach.

First sentence https://en.wikipedia.org/wiki/Parietal_cell.

Looking a little closer at the wiki page, I found the following:

"Hydrochloric acid is formed in the following manner:

Hydrogen ions are formed from the dissociation of carbonic acid. Water is a very minor source of hydrogen ions in comparison to carbonic acid. Carbonic acid is formed from carbon dioxide and water by carbonic anhydrase.
The bicarbonate ion (HCO3−) is exchanged for a chloride ion (Cl−) on the basal side of the cell and the bicarbonate diffuses into the venous blood, leading to an alkaline tide phenomenon.
Potassium (K+) and chloride (Cl−) ions diffuse into the canaliculi.
Hydrogen ions are pumped out of the cell into the canaliculi in exchange for potassium ions, via the H+/K+ ATPase. These receptors are increased in number on luminal side by fusion of tubulovesicles during activation of parietal cells and removed during deactivation. This receptor maintains a million fold difference in proton concentration. ATP is provided by the numerous mitochondria.
As a result of the cellular export of hydrogen ions, the gastric lumen is maintained as a highly-acidic environment. The acidity aids in digestion of food by promoting the unfolding (or denaturing) of ingested proteins. As proteins unfold, the peptide bonds linking component amino acids are exposed. Gastric HCl simultaneously activates pepsinogen, an endopeptidase that advances the digestive process by breaking the now-exposed peptide bonds, a process known as proteolysis."

It seems chlorine plays a role in the exchange of bicarbonate with the cell, but again it moves separately from the H+, which uses a proton pump.

I guess my question really is, if H+ alone was pumped into the stomach, would it have the same effect on the pH we see with HCl? Is the chlorine ion really necessary to the acidic environment?

Thanks for your input everyone!