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Yep, phone cameras are typically way better quality than webcams. You don't even need to use USB, most of the apps just connect the phone to the pc via wifi. I was using an old iphone as a cam until a webex upgrade made webex incompatible with it.
Maybe a daft question, but do you need to use the laptop at all? Skype and Zoom both have phone apps. Loads of people I work with don't bother joining meetings from their laptops, they just use the app on the phone.
Do you need to Skype/Zoom from a computer - basically, do you need to share your screen? If not, just use the phone app. If you are demo-ing/instructing or something, consider a phone tripod.