makes it more of a hassle to update and it puts more strain on the support team.
Uploading the same update to 2 websites adds so much extra work, you're right!
...wait no actually the exact opposite of right. The amount of extra work requied in comparison with the amount of work required to actually make the content is practically zero. Even a single person buying from itch.io instead of Steam, even if they waited for a 90% discount, would earn more than it costs to have the game available on a second platform.
Maybe if we were talking about one of the console devs who have long-winded often multiple week verification processes before letting you update your game, this would be an argument.