An interesting question even a year after it was posted. I would also like to find a solution since USB-C ports are becoming more popular and more capable.
What I have seen are KVM switches with a USB-C connection to the computer but it has a built in dock of sorts that breaks that USB-C connection into USB-A and HDMI ports for keyboard, video, and mouse. I suspect this is popular among people with a laptop for work and a tower computer with a high end graphics card with USB-C for play, or just two laptops pressed into service as desktops. This would be useful for switching between two Macs that have Thunderbolt ports, USB-A keyboard and mouse, and a single HDMI display. Dual displays or other various configurations could leave people wanting more.
Displays with USB-C input are still rare, and those I do see will often times have a KVM switch built into them. If someone looking for a solution is not set on getting an Apple display then shopping for an alternative is an option. These displays will allow for a laptop (or the rare desktop with DisplayPort over USB-C) to plug into the USB-C port and then another computer (typically a desktop) to connect by USB-B and HDMI. The switching between inputs would be like a typical KVM switch with a press of a button on the display or a key macro on the keyboard. My thinking is that implementing a KVM switch in a display like this is merely a matter of software in the display once they cover their bases on supporting old and new hardware with inputs for USB-C/DP, USB-B, HDMI, and an integrated USB hub to get a couple USB-A ports. It costs little to implement a KVM switch in a display so I expect this feature to become more common.
I believe KVM switches have gained popularity with it becoming common for people to have more than one computer at home. What is competing with this though are software solutions. It is trivial to use some screen sharing protocol to create a "software KVM switch". We've seen macOS come with VNC screen sharing server and client for some time now so this may be an option to consider. I've heard of people seeing reduced video performance from this because without a display attached the GPU might not be active, a workaround for this could be called a "display dongle". A "display dongle" is a small device that plugs into a video port to fool the GPU into thinking a display is connected. Even though the video is sent over the network and not the video port there's an improvement in performance because the GPU is doing some of the video processing.
Given that the original question has no concern about the audio and USB being active in the display then it may be possible to use a common DisplayPort KVM switch. The connection to the display would be by a USB-C to DisplayPort cable, or a DisplayPort cable and USB-C adapter. The connection to the Macs would mean using some kind of mini-dock or occupying two USB-C ports, one occupied by a USB-A adapter for the USB keyboard and mouse and the other for DisplayPort video (and likely using the same kind of adapter as for the display since these adapters should be bi-directional). I don't know if an Apple display will work with a DisplayPort input, it should in theory but it seems Apple might be doing things a bit differently than other displays with USB-C inputs.
I realize that's a lot of background but I found it helpful in the past to provide some background up front since there's often questions on why a given suggestion was made. In this case it would be trivial to at least try a software solution first, then if there's issues of performance or convenience then consider hardware solutions.
