Can all laptops with usb c ports charge with a USB C charger?

I'm in the market for a new laptop, and I've noticed most of the newer laptops have at least one usb C port. Some if them like the MacBook, Razer Blade Stealth, and Chromebook Pixle use the port to charge the device, while others like Dell, Acer, and Lenovo have usb c ports (along with other typical ports) and a dedicated charging port. My question is will the laptops with dedicated charging ports also charge through their usb c port? My goal is to only have to carry around one charger for my phone and my laptop.

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