There really is something terribly wrong here. The memory is made to certain specifications, the memory should function correctly at a certain speed with a certain range of voltage etc. The motherboard should provide the correct voltage within that range. If memory doesn't work with 4 sticks in the MB, either the RAM or the MB is not working to spec and is therefore made incorrectly. Companies nowadays never get held liable for making shoddy products.
Well, these memory speeds are advertised as their potential overclocked speeds. With any type of overclock, a lot goes into it, and there are never guarantees. So much comes down to the silicon lottery.
Even with high end enterprise class server equipment, depending upon how many RAM slots you fill, determines the max speed that you are going to be able to run the RAM at. You will find buried in the documentation that if you populate say 6 of the DIMM slots you get 2400, but if you populate any additional slots it drops to 1600, and if you fill the last 4 slots, you drop to 1333.
It's been this way in the consumer area for quite some time with RAM. most times, we get lucky and it just works. We also are told to try to get matching sticks, same make and model works best.
Whether you actually see a performance hit day to day is the real question. On paper, the drop from 3200mhz to 2133 is huge. that's 33%. However, I have a PCI Gen 4 NVMe drive that can hit 7000MB/sec. I also have a SATA SSD that hits 530MB/sec. That makes my NVMe drive 13.2x faster. But when I compare loading and playing games on my system, the difference is like 13 seconds, versus 11.8. It's completely negligible. On paper, it would be night and day. In the real world, you have to prove it via a stopwatch
In your case you have a stated need for more RAM. You could remove your third stick and time your system performance to see if running at 3200 really makes any difference at all. Then you would know for sure if it's really hampering you at all. You may find that it doesn't amount to anything. If that's the case, put in the extra RAM, call it a day and don't worry about it. When you buy your next system, research more on your exact mobo and the RAM you want to run to ensure that others have success.