How to prevent submitting the HTML form's input field value if it empty

This can only be done through JavaScript, as far as I know, so if you rely on this functionality you need to restructure. The idea, anyway, is to remove the name attribute from inputs you don’t want included:

jQuery:

$('#my-form-id').submit(function () {
    $(this)
        .find('input[name]')
        .filter(function () {
            return !this.value;
        })
        .prop('name', '');
});

No jQuery:

var myForm = document.getElementById('my-form-id');

myForm.addEventListener('submit', function () {
    var allInputs = myForm.getElementsByTagName('input');

    for (var i = 0; i < allInputs.length; i++) {
        var input = allInputs[i];

        if (input.name && !input.value) {
            input.name = '';
        }
    }
});

You might also want to reset the form afterwards, if you use a listener and cancel.

You probably don't want to match radio buttons. And if the form contains select's, you'll need to match them too.

With jQuery, you might use something like this:

$('#form-id').submit(function() {
    $(this).find('input[type!="radio"][value=""],select:not(:has(option:selected[value!=""]))').attr('name', '');
});

Instead of using a submit-type input, use a button-type input for form submission. The JavaScript handler for the button-type input should call form's submit() method after checking that commentary is non-empty. You should also alert the user to their mistake (better with a red text on the page rather than the pop-up produced by alert()).

Remember that you should not rely solely on client-side input validation, though since it is always possible to send the form from a modified page or directly in HTTP.

I prefer not to alter the input elements (changing their names, or flagging them as disabled and so), because if you go back you could get a broken form.

Here is my solution instead, which relies on FormData:

window.addEventListener('load', function() {
  let forms = document.getElementsByClassName('skipEmptyFields');
  for (let form of forms) {
    form.addEventListener('formdata', function(event) {
      let formData = event.formData;
      for (let [name, value] of Array.from(formData.entries())) {
        if (value === '') formData.delete(name);
      }
    });
  }
});