Some background for continuity;
The CCV/oil vapor capture scheme is NOT unique to BMW. Every car maker has a version of such fitted to any modern ICE.
This was borne out of tightening emission regulations. Crankcase fumes must not vent into the atmosphere. Same for fuel vapors from the fuel tank, all the way up through the injectors; albeit that's the EVAP system.
So the all too familiar CCV that's discussed here is the regular or cold climate (much preferred by me) version. It does work fairly well, however like anything else on your car it DOES NOT last forever.
Then folks go chasing codes incorrectly, replace a bunch of parts (not CCV related) and codes can sometimes persist. Then more parts get thrown at the car and finally the CCV system was found to be a major contributor to the running issue.
Out of frustration it then gets labeled as a complete POS. Unfair I say because of bad diagnostics. Then folks spend hours doing a modification(s) to eliminate the CCV system. Some successful, others not. Well documented if one searches the posts here.
Lets have a very brief look at how it works; First and foremost the piston rings must be clean and floating to ensure that the engine not only makes good power, but also produces good vacuum and controls oil burning. (Both erstwhile endeavors, no?) Since the CCV system captures the vapor inside the engine and then separates the oily vapor and condenses it, then sends it back to where it belongs; in the oil sump. The (mostly) air vapor is returned to the intake, mixed with the incoming air/fuel and processed by the catalytic converter/oxygen sensors.
If your rings are "coked" up not only are you burning oil, your engine will be lower than threshold for vacuum. Since the CCV system has no electric motors for activation, it uses engine vacuum to make the above operation happen. Furthermore since the CCV system is trying to separate the oil vapor from air vapor AND since your rings are NOT clean, you will produce copious amounts of the undesirable oily vapor. When combined with an old and tired CCV system, it becomes overwhelmed.
Also diaphragms can crack from age, short tripping makes mayo, and drainback tubes become clogged.
There's many ways to check into some information about why your car is not running right. Evaluating fuel trim values, checking (use a smoke tester dammit) for vacuum leaks (remember I said that the CCV system uses vacuum? Therefore if you have a vacuum leak, it's NOT going to work properly!) and having a look at things like fuel pressure and compression health of the engine.
Switch to a M56 valve cover and install a catch can? Sure, but keep in mind you're band-aiding an underlying issue. That also presumes that you've done it correctly and NOT pressurizing the engine??
Tantamount to installing the wrong plugs and coils into the car, it's likely not going to work correctly.
It's a simple system, and may need to be replaced once, maybe twice during ownership. What's the big deal? One wouldn't scoff on two fuel pumps, a couple of water pumps and/or thermostats, BUT the CCV, oh it's a piece of shit. I don't get it?
When a car comes in here for a running fault and/or smoking, we must establish some basics FIRST!
What's the engine vacuum?
What are the fuel trims?
What are the fault codes?
Then we must move forward with the "3 C's": Complaint, Cause, Correction. With a heavy emphasis on the later two.
Looking at fuel trims, making logs and having NZ read them is generous and nice. However the fuel trimming is a continually adaptive scheme. If you haven't checked the basics first you might be replacing many parts that don't deal with the root of the issue, but only addressing the symptoms?
Get the rings clean with SAFE oil & additives, renew the CCV if it's more that 100K miles, clean the double wall dipstick and replace ALL the CCV hoses. It will give you good service.
Rant OFF....