"The insurer just bought the plane"
Occasionally, I read "the insurer just bought the plane" in the context that you're about to wreck a plane, so - worry about yourself, and sacrifice the airplane. On the surface of it, yes. That said, as is also wisely said: "Fly the airplane as far into the crash as possible" = don't give up and just let it crash, knowing/thinking/hoping that the insurer will pay for the plane. Yes, the insurer may pay for the plane, but the security of mind of that should not alter your application of your best skills to prevent/mitigate/minimize[the severity of] an accident. Let alone the duty you have to all of us to do your part to keep premiums low by minimizing claims, there are other longer lasting factors:
If you are PIC for an accident, it is likely that you are not covered for personal injury as a result of that accident. The passengers will be, but not the PIC (and sometimes PIC family members who may be involved). So, as PIC, a paid out wrecked airplane could be a very small part of the financial impact on you - your getting hurt is painful and expensive. And even if you walk away uninjured, if you were PIC for an accident with a claim, you have to declare that on every pilot report for the next many years. That will open up questions about your insurability. That could, in the long term, be more costly for you, than the damaged airplane, depending upon what else to [want to] fly.
For myself, I have been PIC for five events in which an airplane was damaged. One being destroyed. I have never been a party to a hull claim being made. In four of the events, I just paid out of pocket to repair the plane, it was less costly than a longer term premium increase, or worse, a decline to renew. For the destroyed airplane, I was training the owner, and the airplane was not hull insured, so there was no hull claim. He had a agreed to a hold harmless for me (which I insist on for training), and he was flying, so it was a hull loss cost to him - but still very personally costly to me as the official PIC.
On the whole, think about what you want the insurance to cover, and what you may not what to endure from the insurers in the future. I complete a number of pilot reports each year to be covered on customer's airplanes. A low deductible, and small hull claims may not be the best thing for you in the long run. I can and am truthful about my flying history, and happily can say that I have never had a hull claim, nor accident as pilot flying - that resulted in an insurance claim. For 33 years, I did not carry hull insurance on my C150, then I lost it uninsured in a hangar fire - that hurt! I about broke even on the premiums not paid over that period vs the loss of the plane. I had always thought that if damaged, I would just pay to fix it - I did not foresee puddle of aluminum! Obviously in retrospect, it has crossed my mind, that that would have been a good thing to insure it for! So now, yes, I fully insure my remaining airplane. But, for the risk of fuss to my flying record, I really do still fly it as though I am responsible for it, and would only consider claiming for a total loss (not just minor damage).
And, if you are flying a fully insured airplane (well... flying at all...) keep your pilot skill and currency/recency and logs up to date, and if it's your plane, also keep the maintenance records up to date. Insurers do ask after an accident! They don't have to cover a flight which did not meet the legal requirements. If you're in a situation where suddenly "selling" the plane to insurer seems like the only outcome, still try to keep the sale as small as possible - there are many other factors to that "sale" which won't be immediately apparent!