Resizing the system partition is possible, but you need to be S-Off. To really make a difference you don't want to just remove a couple of apps, but to use a much smaller custom ROM. We took that to the extreme in the heyday of the Desire, when one forum member produced a Gingerbread ROM for that phone that you could fit into a 60MB partition (though I preferred to customise it a little, so used a 70MB partition to give myself a little headroom).
You'll find a collection of resources and old threads discussing customising that handset over in our Desire Root forum. The All Things Root Guide sticky post collects a lot of these together. As noted, a lot of stuff may no longer be available, since the peak period for customising that phone was 2011.
Moving stuff to the system partition while running Android also requires you to be S-Off. Or edit a custom ROM zip, adding/removing apps to taste, and then flash it from recovery (but remember that the whole thing has to fit in the system partition, so don't go adding too much!). You might be able to add/remove stuff from system when in recovery mode using ADB - if you are in recovery mode you are not running Android. As I switched to custom ROMs early on it was generally easier to modify the ROM and reflash it.
Whatever you do, don't mess with the system partition without taking a nandroid backup first (a backup made using recovery). And before attempting to modify the size of that partition (if you can get S-Off) make sure you know exactly what you are doing: the way we did that was by replacing the bootloader with an edited version, and if you mess up the bootloader you can end up with an irrecoverable brick on your hands, because all of the tools you would use to fix it rely on having a working bootloader. You can mess about with ROMs because if that goes wrong you just restore a backup or reflash the phone, but bootloader modification should not be done casually.
You'll find a collection of resources and old threads discussing customising that handset over in our Desire Root forum. The All Things Root Guide sticky post collects a lot of these together. As noted, a lot of stuff may no longer be available, since the peak period for customising that phone was 2011.
Moving stuff to the system partition while running Android also requires you to be S-Off. Or edit a custom ROM zip, adding/removing apps to taste, and then flash it from recovery (but remember that the whole thing has to fit in the system partition, so don't go adding too much!). You might be able to add/remove stuff from system when in recovery mode using ADB - if you are in recovery mode you are not running Android. As I switched to custom ROMs early on it was generally easier to modify the ROM and reflash it.
Whatever you do, don't mess with the system partition without taking a nandroid backup first (a backup made using recovery). And before attempting to modify the size of that partition (if you can get S-Off) make sure you know exactly what you are doing: the way we did that was by replacing the bootloader with an edited version, and if you mess up the bootloader you can end up with an irrecoverable brick on your hands, because all of the tools you would use to fix it rely on having a working bootloader. You can mess about with ROMs because if that goes wrong you just restore a backup or reflash the phone, but bootloader modification should not be done casually.