iOS update much bigger on PC

Yes, you will always see this. When you update over the air directly on the device, it is an incremental download/update. The device only downloads that smaller incremental build and then unpacks and runs the installer all on the device itself.

When you do it in iTunes on a computer, it is the entire new iOS image that is downloaded, unpacked and installed. But the download is on the computer, not stored on the device itself. So that big download gets dumped to your computer's hard drive, uncompressed there, and the installer runs on the computer and simply write the changes in iOS onto the device.

Not when it is downloading 1.85GB instead of 0.054GB it's not

For whatever reasons, it is what it is and has always been that way. In some ways it is a good thing, as you can choose to save the downloaded firmware image in iTunes and then update all your iPhones, iPads, and iPod touches without re-downloading the iOS update each time.

It's actually the over the air update that was altered when introduced in iOS 5 - to minimize the download on individual devices so that each device and model only had to download just what it needed.

In both iTunes and the over the air update on the device, once the download is uncompressed and the installer run, the download and all temp files are deleted by the installer itself, as its last act. iTunes will only save the download if you take steps to make sure it does. Otherwise, in either case, everything downloaded is purged from the device or the computer once the update completes.

Why not just do it on the device if that is what you want.