Why did the Allies prioritize invading France instead of massively building up on the Itailian coast after they've already established inland?

The geography.

Italy has some less than ideal terrain for large scale military offensives, it's hilly, with a mountain chain running down the centre and it's narrow, not to mention the Alps that'd block any invasion force that had fought its way that far north. That all makes it easier for a defender to hold the territory and inflict casualties on the attacker with fewer troops stationed there at any one time, plus supplying a significantly increased army presence there would have been more difficult than supplying the same forces in France (after a significant beach head was established that is) because it would have been further away from the sources of weapons, ammunition, equipment and whatnot to keep the war going and their supply lines to Italy were more exposed (U-boats could patrol the approaches to Gibraltar, it would have been harder to suppress the Luftwaffe in the western Mediterranean because of the distances involved).

France's terrain is a lot more open, wider and easier to move a mechanised army around on which favours ~~defence~~ offensive action because it spreads out any defensive forces over a longer distance, plus while there's mountains around some of France's borders there aren't any between France and Germany that can be used stop an eventual invasion of Germany. Britain is really close to France so supplies could be made there, or shipped over from the US and stockpiled there, the same goes for troops, and air support for the invasion could be based there, and distances needed for shipping troops and supplies were much shorter so fewer ships would be needed and a smaller area would need to be patrolled to protect that logistical line (you might think the same thing could be said of Sicily, but Sicily didn't have the infrastructure built up to do that as easily, stuff like roads, ports, air bases, barracks, etc. and building it would have been a lot of work).

It doesn't hurt the decision that the French Government in Exile was largely based in London (until moving to Algiers) and their ability to raise local forces quickly if they liberated France would bolster the available manpower to the Allies on the western front even if there weren't as combat ready as the invasion forces.

Lastly and probably least importantly to the western Allies by that point in he war (although probably more importantly earlier when most of the planning was being done) was that because an attack in France would inevitably have a longer front line than in Italy more German forces would need to be sent there to hold off the Allied attack instead of going to the Eastern Front to fight the Soviets, thereby relieving some of the pressure on the USSR.