Why is an order of execution NOT appealable?

Section 1(f) of Rule 41 of the Revised Rules of Court expressly provides that no appeal may be taken from an order of execution.

Section 1. Subject of Appeal. — An appeal may be taken from a judgment or final order that completely disposes of the case, or of a particular matter therein when declared by these Rules to be appealable.
 No appeal may be taken from:
  1. An order denying a motion for new trial or reconsideration;
  2. An order denying a petition for relief or any similar motion seeking relief from judgment;
  3. An interlocutory order;
  4. An order disallowing or dismissing an appeal;
  5. An order denying a motion to set aside a judgment by consent, confession or compromise on the ground of fraud, mistake or duress, or any other ground vitiating consent;
  6. An order of execution;
  7. A judgment or final order for or against one or more of several parties or in separate claims, counterclaims, cross-claims and third-party complaints, while the main case is pending, unless the court allows an appeal therefrom; and
  8. An order dismissing an action without prejudice.
In all the above instances where the judgment or final order is not appealable, the aggrieved party may file an appropriate special civil action under Rule 65. The basis for the rule prohibiting appeals from orders of execution is the doctrine of immutability of final judgments. Under this doctrine, a final and executory judgment, however erroneous, can no longer be amended, modified, or set aside, whether by the court rendering it or by an appellate court.

The doctrine "is grounded on fundamental considerations of public policy and sound practice" that litigations should have a definite conclusion at a given time even at the risk of occasional errors. As this Court explained in Gonzales v. Solid Cement Corporation:
A decision that has acquired finality becomes immutable and unalterable. This quality of immutability precludes the modification of a final judgment, even if the modification is meant to correct erroneous conclusions of fact and law. And this postulate holds true whether the modification is made by the court that rendered it or by the highest court in the land. The orderly administration of justice requires that, at the risk of occasional errors, the judgments/resolutions of a court must reach a point of finality set by the law. The noble purpose is to write finis to dispute once and for all. This is a fundamental principle in our justice system, without which there would be no end to litigations. Utmost respect and adherence to this principle must always be maintained by those who exercise the power of adjudication. Any act, which violates such principle, must immediately be struck down. Indeed, the principle of conclusiveness of prior adjudications is not confined in its operation to the judgments of what are ordinarily known as courts, but extends to all bodies upon which judicial powers had been conferred.
ADDITIONAL READINGS:

 [1] Provincial Government of Aurora v. Marco, G.R. No. 202331, April 22, 2015 [Per J. Leonen, Second Division].
[2] King Integrated Security Services Inc. v. Gatan, 453 Phil. 293 (2003) [Per J. Sandoval-Gutierrez, Third Division], citing abular v. CA, 204 Phil. 654 (1982) [Per J. De Castro, Second Division].
[3] 697 Phil. 619(2012) [Per J. Brion, En Banc].
[4] Mocorro, Jr. v. Ramirez, 582 Phil 357 (2008) [Per J. Velasco, Jr., Second Division].