The "island hopping" strategy was designed to both cut the Japanese mainlands off from the resources it was extracting from other nations (like the Philippines), destroy its naval dominance, and also to create footholds for making said major aerial attacks (and eventual amphibious invasion) against the Japan home islands. They could not have dropped the atomic bombs — or conducted the ~70 other major firebombing raids — against the Japanese mainland without a reliable, defensible locations from which to attack and supply their planes. This is what they "got" from taking those islands, places like the island of Tinian which they turned into a massive airfield that could launch +500 B-29s against the Japanese mainland (same with Okinawa, and several other places).

Now, they could occasionally skip islands and just cut them off and let them wither. Which they did in some cases where taking the island was deemed more difficult than what they'd get from it (like the island of Truk). But generally speaking they took the islands as a way to get closer to Japan, and to destroy the Japanese ability to project naval and air power.

They had looked at other ways to strike Japan — e.g., from China — but they were much more difficult logistically (e.g., to get supplies into China you have to fly them from India, around the entire other side of the world). Logistics matter in war — how much firepower you can put in the field is what determines the outcome in the end.

They could bomb Japan without the islands, but it wasn't very effective. The Doolittle Raid, for example, involved bombers launched from aircraft carriers that bombed Tokyo and then continued on to China and Russia for landing (mostly unsuccessfully, but most crews survived). That's a very ineffective and inefficient way to try and attack a country, and was more for morale/psychological warfare than real strategic outcome.

Quite simply, the Pacific ocean is huge. Circa 1941, no country had the resources and equipment necessary to make an opposed landing and then support that invasion of mainland Japan from all the way across the ocean. Even if such resources existed, the Japanese either already possessed or immediately captured all of the island chains such an invasion fleet would sail past, and would have been able to attack that fleet from the air for days before it would reach striking distance of Japan. Certainly at the time, and still true today, carrier aircraft are smaller, have shorter ranges (without refueling), and carry lower payloads than land-based aircraft. Thus any strike force would be forced to attack against Japanese aviation that outraged it.

It is one thing to pull off a single surprise attack at long range with a few ships and special aircraft like the Doolittle raid, it is very different to launch a massive invasion fleet whose exact location is known by the moment the first soldier hits the beach. Even in 1945, with better ships, aircraft, radar, and doctrine, the allies suffered significant losses supporting the invasion of Okinawa against a much weakened Japan.