I remember the frustrations of doing your job, OP.
The flight cancellation/delay aspects of Insurance is to cover for such things as volcanic eruption, hurricane, flood plague of locusts, yes really, engines falling off on the tarmac, etc - but not for what the airlines term 'operational reasons' or companies going bust. Insurers aren't there to prop up shit personnel policies or inadequate financial husbandry; liabilities for those are covered by law.
From those blurry 19 hour days of handling claims in my past, the advice I'd give is;
Don't assume that because your GP says 'have a lovely time, a holiday's what you need' he means you're fit to fly and Insurers will cover it. They say that to everybody - including people who are so ill that they end up being resuscitated mid flight. Check the wording, declare the condition, have cover confirmed in advance.
Don't assume that because your appointment at the hospital is six months away that you'll be covered. Declare it. Because Sod's Law dictates that whatever it is you're on the waiting list to be seen about will suddenly worsen after you cross the gate. And then you aren't covered.
Don't assume that having a shit time means the Insurance company will give you all your money back to make you feel better. Loss of enjoyment of your holiday is not an insurable risk. particularly when the entire coach trip party is claiming for a full refund of the holiday because they got seasick and panicked once out of the bay because a really big boat went past
Don't get pissed and fall over. The hospitals tell us. Not too traumatic financially when it's a simple sprain, but if you've broken your ankle, need emergency surgery and to stay for another fortnight until you're safe to fly, the fact that you'd done it whilst performing the Macarena on a six foot high wall means you're going to have a very large bill. And if you go anywhere near the water or climbing balconies when under the influence, your next of kin could have far, far worse to deal with.
Pregnancy is not a reason in itself to cancel a holiday. If there's a complication and the doctor confirms that it is not safe for you to fly or you're outside the airline safe/legal weeks for travel, no problem. But get the insurance before you get a BFP. You do not want to be the parent of a preemie in the US when you only bought the insurance the day before you travelled at 35 weeks - or if you've got twins on the way, 31.
Don't put anything up anybody's arsehole or your fanjo. Just DON'T DO IT. And if you do, don't try and claim for a bout of cystitis. We will know.
Use sunblock, wear a hat and don't fall asleep for four hours on the beach. You're going to hate the rest of your holiday.
Other than that, don't pack expensive/fragile stuff in your suitcase, don't carry food or big bottles of sunblock in there and whatever you do, don't leave your camera and all your jewellery under a beach towel and go off for a swim. Or try claiming for a Louis Vuitton suitcase, £3.27 above the total sum insured for baggage in clothes and a pair of Dolce & Gabbana sunnies when your suitcase cost a tenner from the market.
It's easier and quicker for the person dealing with the claim to pay it than have you shouting at them down the phone. And most of us that have handled claims don't particularly like telling you that you're not covered, especially when we could have just been on a call to a distraught 89 year old whose husband has just died and went over our allocated time for a call (which we will get into trouble for) because she needed to hear a friendly voice explaining what we needed to be able to get the payment authorised - but then get you and you're shouting about your socks being covered in Ambre Solaire.
They can't pay what isn't covered or isn't evidenced - give them a chance to do the easiest thing.