It is 100% sure that all 4 USB-C ports of MacBook Pro 16'' 2021 supply DP Alt Mode, but there is still got chance that you can not use the USB-C to HDMI Adapter normally. Please confirm your UBS-C port function well, and the HDMI to HDMI cable works properly. If the above all performs well, you should consider changing the adapter.
Oh, yes, one more tip for MBP users . You have to charge MBP when you want to activate the clamshell mode, before closing your screen.
And for Windows Users, please make sure you've got the latest driver. (Or you can view the troubleshooting here.)
Make sure your USB-C device is all up to date (get the latest drivers).
This often happens when you use the adapter/cable for a while (3-12 months), or immediately appears after you upgrade the system; It most frequently appears with Windows users when upgrading to Windows 10/11.
For Windows users, if your USB-C to HDMI adapter is not working, the issue might be connected to the dedicated driver. So we recommend you update the USB to HDMI driver on the official website. Alternatively, recently installed Windows 10 updates can lead to problems due to random bugs. Well, at last, the problem might also be the hardware itself, which means the adapter itself.
And for the rest non-Win Users, there is still a chance that the system or the CPU causes the problem.
However, go and contact your devices manufacturer and the adapter provider will always get an answer.
3. Distracting Screen Flicker.
What you should do first:
Tried a different cable/adapter.
Then Tried a USB-C DisplayPort cable (if you have DP port in your external display).
Well, actually chances of encountering this issue are way more than the rest of the problems. Some people just ignore this. However, there will be two reasons causing this happening.
A. The connection from USB-C to the display has errors. It might be the adapter went down, the HDMI to HDMI cable is not good quality, the HDMI cable length is over 15ft, or the display goes faulty on refreshing rate(even without any other connection), and there is also a slight chance that the host device (USB-C device) is not working well.
B. Other connections affected the display, besides USB-C to HDMI. Maybe the power output of the HDMI display causes unusual surge.
Some people might consider this issue as Compatibility faulty, things like different protocols created by whom.
However, I believe the most important thing is you need to figure this issue out, get rid of the flickering.
Just confirm directly with the USB-C device manufacturer this professional question.