It can be tempting to just smear a glob of joint compound into a frustrating gap between wood and drywall. Many people do use this type of material as a filler. Unfortunately for them, they usually find that the resulting structure cracks not long after. Here are a couple reasons why this happens and the means to overcome the problem.
Joint Compound Filler Creates Dimensional Instability
The biggest reason why the drywall and wood cannot have joint compounds in between them is that they both swell and shift shape with changes in the home's RH (relative humidity). The home's RH is greatly affected depending on the seasons, the weather, and the temperature. This leaves you with a joint compound that is unstable due to the different types of materials and their different characteristics ending up causing the joint to crack from the shifts in each material. While it may make for a temporary fix, this is not something you want as a permanent or long term fix. Most of the time, the cracking occurs pretty quickly.
Joint Compound is Designed for Covering, Not Filling
The other reason is the fact that a joint compound is mainly designed to bring two side-by-side surfaces together as one when the compound is applied in a rather thin coat that adheres a paper tape or a mesh to each surface by covering the space in-between them. The tape adds stability and rigidity to the joint keeping all of its components in place thus creating a solid and stable joint built up with successive thin coats of drywall compound blending the two surfaces as one. The drywall tape with its added rigidity is what keeps the drywall assembly together and without cracking.
When you try and fill a space or a gap with ample amounts of the compound, however, the added amount tends to create a blob of it that becomes more and more fragile with size. The compound becomes extremely brittle and has no flexibility or elasticity whatsoever. Without the drywall tape, the drywall and the wood are both bound to dimensional changes, and without any give from either because of lack of elasticity, the joint cracking is a certainty.
How to Properly Fill Drywall Gaps
You can succeed, however, in getting the perfect joint between wood and drywall. Make sure that you attach both the drywall and the wood with plenty of drywall screws (not nails), cover the wood with primer, and then plaster the joint as you would plaster a regular joint, using drywall tape and compound. If the joint is too wide to be covered by one strip of tape only, start with one and keep adding strips successively overlapping to cover it all while it is still wet unless the gap was wide enough to patch with a strip of drywall which is what should be done in that case.
Be careful however to keep using real thin coats of the compound at a time as to not create a lump that would be difficult to sand back down.