That's significantly more complex than goal-line technology, though. Instead of simply monitoring a relatively small two-dimensional plane in a three-dimensional space and check if the ball has crossed it, you're looking at monitoring a three-dimensional space that's as long as one half of the pitch, as wide as the pitch, and has significant height.

The cameras used for the goal-line technology are already covering all of the pitch in 360 degrees. None of that is an issue.

You'd then have to account for the way the offside line changes constantly

That's an example of what computers do very easily, humans not very well at all.

keep the players and their limbs apart

Not a problem. The system is already capable of seperating the ball from players, even if the goalkeeper for example is holding it tightly in his arms.

monitor the ball across the whole pitch and be able to pinpoint the instance it leaves a player's foot

Again, trivial tasks for a computer.

And that doesn't even account for things like deflections or the ball pinballing between several players without them having any control over where it goes

It's trivial for the computer to keep track of who is touching the ball, and ther rule makes the decision very simple.

All of the issues that you outlined are the easy ones to solve. The difficult one is deciding things like who is effecting the play, but even that would be relatively simple to have the system be at least as good as humans and way more consistent.

I'm ignoring the money part since...well, I already mentioned it and my point was that technology is not the issue.