Reading through the issues you filed I agree, explicit *With seems like a reasonable requirement if you really want context.

For most code I can't imagine any useful purpose in having the promise available as context. One would always chain on the promise directly, create a new deferred, or involve other code that produces a new promise. One wouldn't call then() inside the then-callback of the same promise.

However, there is be one jQuery-specific use case that applies to inside callbacks: state().

$.Deferred().reject().always(function () {
  console.log(this.state());
});

I don't expect this in more advanced projects, but I wouldn't be surprised to see in simple projects.

/** @return {jQuery.Promise} */
function foo() { /* .. */ }

showSpinner();
foo().always(function () {
  hideSpinner();
  if (this.state() == 'resolve') {
    // Stuff...
  }
});

It seems awkward to have to store the promise in a variable for that.

The following use case was rather counter-intuitive to migrate when using only the text on https://api.jquery.com/jQuery.Deferred/ and https://jquery.com/upgrade-guide/3.0/

function postWithToken(type, params) {
  return api.getToken(type).then(function (token) {
    params.token = token;
    return api.post(params).then(null, function fail() {
      if ( code === 'expired' ) {
        return retryOnce(type, params);
      }
      // Let caller handle any other error
      return this;
    });
}

Initial attempt:

-    return api.post(params).then(null, function fail() {
+    return api.post(params).then(null, function fail(err) {
       // Let caller handle any other error
-      return this;
+      return err;

I tried this because I previously believed that a then() kept the current state if a non-promise is returned (plain value from resolved then is resolved, plain value from rejected then is rejected) - and that creating an explicit Deferred is only needed to change the type from resolved to rejected. However for this case, the following fix is needed:

-    return api.post(params).then(null, function fail() {
+    return api.post(params).then(null, function fail(err) {
       // Let caller handle any other error
-      return this;
+      return $.Deferred.reject(err);

This works but recording it here in case it helps someone else, and in case documentation can be improved.