There was no reason to continue the war:
a. Ideologically, Hitler objectives towards France were to retake the "German" (Alsace and Lorraine) land back into the Reich. From a practical point of view, France was no longer a threat, and a likely-minded regime was set in power. The treaty gave Germany everything they wanted.
b. Despite the fast success, the German campaign was not "a walk through the park". There were significant losses (including 1200+ planes and 700+ tanks), and the French army was still a fighting force (with more experience as the war progressed). The faster the campaign ended, the faster those loses would stop.
c. There was still a war going on. Until France was taken out, any attempt against the UK would have to be delayed. If it lasted long enough, autumn and winter would set in making any crossing of the sea very dangerous.
France had other options. The governments of many of the occupied countries had fled to London, transfering whatever assets they still controlled to the Allied war effort. In the case of France, these assets were considerable (its colonial empire2, its fleet -both military and commercial-, as many soldiers that got to evacuate).There was even a proposal of an Anglo-French union3, uniting both countries (so the fall of the "continental" French-UK country would mean not the defeat of the country).
The armistice gave the French an acceptable treaty3 to agree and avoid such scenario. It also kept the French colonial empire inside the German area of influence (even if not under direct control).
It eased the German burden of occupation. It would not need to garrison Vichy controlled zones, and in all of France Vichy police forces and administration continued to operate. A French functionary could refuse to collect tax for the Germans in order to avoid being later considered a traitor, but would have it better if he were collecting taxes for the French government (even if the French government used it to pay the German occupation forces).
Note that France was not the only collaboration government; even in countries who could not retreat to their colonies (Norway, Greece, etc.) collaboration governments were setup to make German control easier. The exceptions were mainly "German" (i.e. directly annexed) areas and in the East (who was to be depopulated anyway).
As for disavantages, putting assets in other people hands always carries the risk of these people switching sides. That said, until the fall of the Vichy government, most of the French siding with the Allies did so as a personal initiative, and I have found no claim that the Vichy government did ever consider joining the Allied side again. At least, the Germans prevented the worst case scenario of the French fleet passing to Allied control.
1 And of course, the always pending question of expansion towards the East.
2 For example, the Allies had to mount an invasion of Madagascar out of fear of Japanese submarines refuelling there, battles were fought for Dakar, Gabon Syria and the UK attacked and sunk the French fleets at Oran and Mers-El-Kebir.
3 The French government refused it.
4 It was harsh, but if you compare it against the Versailles treaty imposed to Germany twenty years before the only significant difference is the occupation of the Atlantic coast, and that was a wartime measure that could be even considered as a measure that helped the defense of the French (Vichy) government.