"No, there is no causative data to suggest that,"
That's just wrong. There is research into how screens affect a young brain, how a child's language develops, how watching a TV or having a TV on in the background affects communication between parents and children and how cuts and the change of sceens in programmes affect attention and concentration.
"there is correlative data [...] To actually find out, we'd need some proper testing of the hypothesis, and controlling for the good/bad parent would be difficult anyway, it might be true, but there is certainly not the evidence to support your dogmatic assertion."
I have to disappoint you, but of course that's been done. Do you seriously think the scientists conducting research simply haven't thought that maybe other things in a child's daily life, except the TV, might affect it's development?
"It really is much more complex than “scientists in different fields agree”."
No, actually it's not. These are people who studied in their respective fields for years, they are experts in their areas and doing research like this is their job. If close to 100% of those dealing with this topic agree on something, you should simply believe it.
I think it's quite arrogant and - frankly, stupid for a "normal" person to claim that this research is wrong, arguing that the scientists conducting that research haven't taken into account the most obvious of things, use some personal stories like "I did that, everything is fine" as "arguments" against it, pretend like all those scientists just want to scare people and make them feel bad (for whatever reason, probably they are being paid by someone to say that) and then give advice to other people based on that, being convinced they are much smarter than the people who do this for a living.
This puts you in a league along with anti-vaxxers and manmade climate change deniers.