Not if robots are cheaper than the poisons.
Your point about insurance is interesting, the industry would do a massive backflip on pesticides if some robotics company managed to convince insurance companies that using their product was less risky than chemical means.
No, now you pay for the service AND they sell your data.
Companies will take every edge they can legally hold.
It's not robotics or chemical, that's a false dichotomy.
And yes, I am aware of the "tradeoffs" of organic farming. But it still is a viable business plan, often the farmers' margins (at least in west EU) are much higher than "chemical farming". And no, not always is the yield lower. Nor are the crops it always more expensive. And no, the common conception that "we cannot feed the world with organic farming" is also disproven.
Looking forward to having more advanced robots, we could start seeing a lot more permaculture. Organic farming not only relies on pesticides and herbicides but also on monocrops and tilling all of which add up to a lot of problems. Robotic tending could eventually allow more diverse permaculture to take over.