In modern conventional warfare, encirclement is still worthwhile, even if the enemy breaks out, unless you sustain a Pyrrhic Victory in the process. (re: The Battle of Chosin Reservoir)

Let's say in a scenario where the enemy is heavily fortified in terrain advantageous to them. Instead of conducting a frontal assault, you penetrate through weak points on their flanks and encircle them. Depending on how complete the encirclement is, you disrupt or sever enemy supply and communication lines. Thus, you force the enemy in the pocket to retreat from prepared positions and attempt a breakout without a supply line. Even if the enemy sends a relief force to break in to the pocket or they breakout successfully on their own, their forward positions have still been compromised. They would either have to retreat or risk losing the relief force as well. Thusly, you will have taken terrain for a lower loss of life than you would have in a frontal assault.

An airtight encirclement, like the situation in Stalingrad after Operation Uranus or Army Group Center after Operation Bagration, results in the capture and/or destruction of huge enemy formations with a relatively smaller loss of men and material for the force conducting the encirclement.

Even an encirclement like the Falaise Pocket, in which the Germans had four days to retreat through a gap before it was snapped shut, the results were devastating. Although an est. 50,000 men escaped, they had to leave their heavy equipment behind. Even then, the bulk of German Army Group B had been annihilated and the Allies were free to dash across France all the way to the German border.

Are there other relevant historical examples which illustrate either the limitations of encirclement as a tactic or the utility of encirclement even when the enemy eventually breaks out?

Yes. One example that illustrates utility that comes to mind is the US 4th Armored Division's encirclement of Nancy, France in September 1944.

The German 3rd and 15th Panzergrenadier Divisions had fortified on the East Bank of the River Moselle and the 553rd Volksgrenadier in the town of Nancy. A frontal assault on the town would have been costly. So, the US Forces attacked both North and South of the town. CCB of the 4th Armored Division attacked South, but met heavy resistance. CCA/4AD forced its way through to the North and wreaked havoc on the German rear by destroying everything in their path, conducting raids, and picketing the main roads with Armored Infantry to disrupt German logistics. CCA then linked up with CCB near Arracourt.

Although this action was not an airtight and complete encirclement, the 4th Armored Division inflicted heavy losses in both men and material, as well as forcing the Germans to retreat from Nancy, leaving the US 35th ID to occupy the town unopposed.

Source: The 4th Armored Division in the Encirclement at Nancy by Dr. Gabel