Hello everyone,
I am trying to understand why carbon fiber components in BMW 7 series and many other cars are used in conjunction with Steel? Why are carbon fiber stand-alone components not used instead of these hybrids? Are there any intrinsic problems with stand-alone carbon fiber components? 

The biggest drawback that I can see is that once carbon is broken, it's broken. It has an elastic performance near 0, whilst steel might be heavier but it maintains very good performance past its tensile strength due to its high elastic performance. In an application like a vehicle pillar, this could be extremely important in ensuring crash safety. Say in the event of a roll over for example, carbon fibre pillars are very likely to break and give no more strength to the vehicle structure whereas steel will continue to absorb energy and is unlikely to completely collapse. 

The hybrid structures are likely based on the idea that the steel is there to absorb impact energy in a crash situation, whilst the carbon gives rigidity and lightweight performance in everyday situations. As for the cars utilising solid carbon structures, I'd hazard a guess that those manufacturers have completely redesigned the crash structure of the car so that it dissipates energy to other areas in a crash and doesn't rely on the pillars for protection.

Of course costs vs design spec are also going to be factors in this as well.

I would like to mention, that carbon excellent elastic propertys, but isn't very malleable. Although you can achieve highest energy dissipation with carbon crash elements (f1 monocoque) they have to be designed in a a very specific way. That and standards and regulations that were made with metal construction in mind, lead to the fact, that it is quite hard to establish a full carbon safety element.

High costs is really no simple answer. There is much more to it than you might think. And doing it as a hybrid structure isn't always the cheaper way.

Carbon crash structures: the basics are pretty simple: metals can convert kinetic energy to heat by getting deformed. And this doesn't mean elastic deformation like a spring, as this only stores the energy. think of a spring falling to the ground. It bounces back. This doesn't help the passenger of the car, as his momentum does simply change his direction. After the drop, the spring will look exacly as before. The deformation was not permanent, but elastic. Now think of a spring made from soldering wire. It will bounce back far less, because the permanent deformation of the lead will convert the energy to heat.
carbon is very bad at permanent deformation (but excellent at elastic deformation (high end bow limbs are made of carbon)), and so can't dissipate kinetic energy to a purposeful degree. But it has a trump card: it can store up great energy through elastic deformation, than snap, and let the stored energy fly away with the broken pieces. Sounds bad? Is bad! This means carbon can dissipate kinetic energy the better, the tinier it breaks into pieces. The energy is converted to surface energy. Now look at a f1 monocoque crash test. You will see, that the mocoque will turn to dust, beginning from the nose.
And here be got our car pillar. Can you think of a way, to turn it into dust as much as possible, no matter how the crash looks like? If you know the direction yes, you could place a tube like structure in that direction, and if done right, it will work excellent. But in a complex structure, with the windscreen and the roof, and with so many possible crash situations, this is really hard.

A f1 tub and a nose are grey specific in their design that they have to pass 1 set of rules in a very specific crash test and the squeeze tests.
Lots of " cheats" that go on
8.1 Ali core used for example in the squeeze area.
You could never make a hole tub with it but easy to put in your test points
Your nose,the very front is cosmetic as it will be destroyed in a nano second so people don't bother doing a structural build to the tip
Not unknown for wing fixing inserts to be missed out in a crash box.
In a crash test solid carbon or Ali inserts can plod through core like a snow plod
You have to crash within the deceleration curve so if you took a cross section of a nose you would see varying thickness laminate.
The same with core and differing densitys