Is the double boiling canning procedure really necessary?
These various boilings serve different purposes.

The jam mixture is boiled to reduce the liquid and bring the pectin to its gelling temperature.

The bottles and lids are boiled to sterilize them as you said.

The final water bath kills any bugs that were introduced while filling the jars. Additionally this boiling ensures a good seal on the bottles. In the time it takes to fill the bottles the jam will have cooled somewhat and you might not get a good seal.

Killing bugs with boiling is not an instantaneous process. It takes time at those high temperatures to kill a high percentage. If the bottles aren't pre-sterilized then you are putting yourself at a disadvantage as those bugs would be distributed through the hot, but no longer boiling, jam.

Of course, all of these boilings will do some sterilization and are somewhat redundant. It's all about reducing risk. You can bottle with clean but unsterilized bottles and if you work quickly you can skip the hot water bath. Doing so will greatly increase the chances that one or two bottles might not seal or that some bug might survive and spoil your stuff. Reliable sources indicate that if bottles are not presterilized that the bottles should be processed longer in the water bath.

Anecdotally speaking- I have in the past skipped the water bath when my jam was very hot and acidic. I would usually have one or two bottles out of 20 that wouldn't seal. I no longer skip the water bath and I almost never have any bottles that fail to seal.

I have never had jams go bad but this is more luck than proof.