What happens if you use a mouse instead?
Thanks for ther reply. The issue is present when using a mouse and a stylus. In the video I am using a mouse.
Does it help when you turn on Smart Guides?
They will at least tell you when you have hit the handle exactly.
Hey. Thanks for the tip. I've checked and turning on Smart Guides seems to resolve the issue. It's not to do with user accuracy though – Illustrator seems to register the click on the handle better when Smart Guides are active. I've found a better solution that I'll post as a correct answer.
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Just do it, if you want it improved.