Modeling is certainly much better than it used to be...I don't think there can be any argument about that. However, IMO I think the rate of improvement has definitely slowed some over the past 5-10 years. That s just my opinion though and I have nothing to really back that up. I'm sure all these model scores and graphs will say otherwise.
As we all know, modeling and the atmosphere is extremely complex. For models to do what they do is beyond impressive. Ultimately, though I don't think models can be technically "wrong". The solution of a model is based on how the model is evolving the atmosphere and all the pieces. Now the model can be wrong in how everything evolves but that doesn't mean the output is wrong.
In terms of forecasting, I think it really comes down to experience, knowledge of fundamental forecasting, and at least a basic understanding of atmospheric physics. Forecasting is just more than looking at models and interpreting the output. It always makes me cringe when people will say "models will change" or "nobody knows what models will do". Those who have a superior understanding of the physics can probably gather better insight into which model may perform better or why one model is struggling versus another.
Expectations and society also play a big factor. Now, everyone wants pinpoint and detailed forecasts for a specific location 3-4-5+ days out. That is not realistic in many situations. Social media has led to irresponsibility sharing information and products (i.e. snow maps) and expectations and reality become distorted.
You're totally right, there is no easy answer but it is a combination of so many different factors, but it is indeed an interesting discussion.