I think your claim that corporate profits -----> is extremely reductive, and probably not even really applicable in the modern context of today. We've seen the highest corporate profits ever over the last decade or so, so we should see innovation proportional to that if it is as one-to-one as you're claiming. But I'll let you discuss that with Broke Wave.
But let's say you're right. How exactly are you defining and quantifying "innovation," and are you assuming that innovation is always good for the economy as a whole? I ask that because there's plenty of innovation going on, particularly in the financial sector...we saw how that panned out.
"Innovation" often can take the form of methods that allow corporations to maximize profits while doing less and requiring less labor. Innovation in many industries means using technological, manufacturing, and servicing practices to cut labor costs.
People need JOBS right now. They need livable wages and lowered living costs. What is "innovation" going to do about that? Because right now, we're increasing moving toward a society of a few technocrats and many serfs.
I've discussed the profits --> innovation long enough. I'll just say that I never claimed it was a one-to-one relationship. That would make little sense. Clearly $1 dollar in profit doesn't translate into $1 in spending on growth and innovation. Also I cited not one but two academic journals supporting the same claim as I did. Anyone who thinks the relationship doesn't exist, the burden of proof is now on you to find me two academic journals which says there is absolutely no causal relationship. If you find them, I will concede. I am open to saying I'm wrong when proven so. I've done it before in other threads. But seriously, I found economic journals agreeing with my basic point.
As far as how to define innovation, I don't have a technical definition for innovation. Whatever I say will probably be picked apart because I guess that is fun for some people. But roughly speaking it's an improved way of doing something that gains widespread acceptance.
You asked "Is innovation always good for the economy as whole?" I would say definitely no. The financial innovations you mentioned are a classic example. Wall Street firms maliciously inventing products to defraud consumers. Yes, that kind of innovation is bad. New innovative 'precision' military weapons that kill civilians with no fukks given are bad in my opinion. New innovative illegal drugs which rip the skin off of off people is bad in my opinion.
But yes, I do think
most innovation is positive. Medical innovation, vaccines, computer procession speeds, machines for manufacturing, airplanes, cars, light speed rail, and on and on. Good stuff I think.
For your last point about people needing JOBS. I agree. What will innovation do for that? Innovation won't do much for that in the short term but recently I heard someone make the point that during the Industrial Revolution, 70% of the economy was farming. All these farming machines came around and started taking jobs away from farmers and people living through that time said, "This is terrible! These machines are taking our jobs. We must stop this. How will we go on?" Looking back I don't think most of us would say they should have stopped the Industrial Revolution so that farmers could keep their jobs. The world changed and eventually we were better off for it. Now we only need 1% of the population employed as farmers to create enough food for the country. So innovation leads to difficult transitions. People have to find new jobs. It's ugly. I think the government has a responsibility to do what it can to find people jobs in the midst of technological growth.
But innovation will make today's technology cheaper and it will lead to greater health and longer life expectancy

. These are good things. Once again, I am not making an all or nothing argument. I wish you all could see that. Are there drawbacks to certain types of innovation? Sure. But in the long run, I think we are better off.