I’d say you’ll definitely get it to work somehow without the kit, but you’re a bit on your own if minor or major incompatibilities show up. (And I would not expect the bare phone to come with a suitable cable).
So, for personal use I might try that, but for professional use the risk of wasting time to get it working smoothly might be a bit too high (I don’t want to sow doubts, it can of course work just perfectly well if you already have a screen (or adapter) for HDMI over USB).
On Bluetooth: I think for the phone they have free drivers available. But I still advise against bluetooth for this intention. If you plan to dock/undock the phone at least once a day, do you really want to plug the USB and additionally take care bluetooth is active and the proper devices are paired?
It’s of course good you can do that, but I’d just want to plug it* in and be ready to go.
*it: The screen via USB-C, which itself is also connected to mouse and keyboard, and of course possibly external disks etc.