But deciding to pay for insurance, and specifically choosing NOT to insure the first 60 days seems penny-wise and pound-foolish to me.
I mainly buy AC+ for the longer warranty coverage. Whether there is insurance for those 60 days is of no concern for me. Apple forces to pay for insurance even if you just want a couple years of warranty. On an iPhone I really don't mind the extra insurance, it might come in handy, but I rather have 2 extra months for free. I take good care of brand new devices anyways, usually I start being a bit more careless after a few months, and maybe a couple years in something breaks. But the first 60 days are irrelevant to me.
Of course if you are buying a brand new expensive 15 Pro and you go on a weeks long vacation right afterwards where there is a much higher risk of trouble then it makes more sense to buy the insurance immediately.
Can you claim for any accidental damage that occurs from dropping it etc?
Yes but it needs to impair functionality. Scratches don't impair functionality but if your display no longer works or front or back glass is cracked, or obviously if the entire iPhone is dead, then it counts.
For my iPhones what usually happens is that I take extra good care of it when it's new, in the first year, and then later I start being a bit more careless and eventually something breaks and I just request a new refurbished iPhone through the express replacement option. That takes care of all the scratches as well as you get sent a new iPhone that is basically like brand new. Costs at most 100 bucks, depending on the damage it can be as cheap as 30 bucks. The funny thing is not once have I used the express replacement because of dropping my iPhone, it just started malfunctioning a couple years down the road on its own. Hence the express replacement was free for me.