It's certainly possible to automate experiments. In fact my job is developing equipment for this purpose, and all of my own experiments are controlled by code. Most measurement instruments have run on code for decades. You don't manually turn the knob on a Wheatstone bridge to measure a voltage any more. A yellow handheld device with a LCD measures it with greater accuracy, or a probe that plugs into a computer. The code living in an experiment like the Large Hadron Collider is extreme.

The distinction between theory and experiment is somewhat arbitrary. Historically, scientists were better at one than the other, with a few rare people being known for both. To make an analogy, there's also no immovable boundary between hardware and software, since most hardware runs on code, but these tend to be different jobs and even departments.

What tends to happen in science is that when a subject is virtualized, e.g., when it can be modeled by a satisfactory theory, scientists move on to new frontiers. Many of the most interesting areas of work are where both theory and experiment can challenge one another.

I've had managers and even engineers ask me in all sincerity why we still need to make measurements when we can just model the data.