Like you, when I'm doing design work for a client, I generally start out with a fairly simplistic model although depending on what changes I anticipate might be needed, I will use a combination of individual components and some more simplistic modeling. Instead of drawing all the parts and then assembling them, though, I draw all the parts in place. So, for example, if I were drawing a cabinet, I would start with the left side, copy it and flip it to make the right side which I would put in the correct location. From there it's a very simple matter to draw the parts that go between the sides to fit. There's no need to figure out how long those pieces need to be. I let SketchUp tell me that when I've completed the model.
It is possible in SketchUp to (and some people do) draw each piece separately and then assemble the parts to make the 3D model.
Is it possible in Solidworks to follow a similar work flow?
In case there's any interest, there's an old video here. that shows that.
You can do that in Solidworks as well, or just edit one part while it is in its assembly. I think most folks will never use all the features of Solidworks as it is pretty advanced. For all my designs I use a feature which allows an automatic update of all the part dimensions. For example if I want to stretch or shrink a Kitchen cabinet to fit in a specific space, I can change one dimension and it will update all the rest including drawer dimensions etc. Or I can go further and allow only standard door and drawer sizes, then the program will attempt to fit the whole job to the new dimension, using standard component sizes.