Modelling is a key activity of engineering - it allows predicting the behaviour of a final system. Linear systems are handy because they are scalable. A bridge to hold 10 people can be scaled to hold 100, 1000, or 10,000 people (usually) quite easily. A software processing scaling from 10->10,000 will often fail in all sorts of interesting ways in the process.
Software often fails silently. In mechanical systems, there is often noises, vibrations, or yielding to give warning and insight to where problems are happening. Software often doesn't have this inherently, but can be overcome with debugging and testing.
I think a large part of this is the newness of the field. People were building bridges, houses, and carts long before Newton. But after we had the modelling tools and theory, we were able to go much further.
(I'm a mechanical engineer, who tends to do a lot of software for controls and models, and increasing web development)