Reddaisy, I don't think people did just cope and find the money when it was needed. I'm a cat rescuer and in my experience I see that this doesn't happen. I get countless pleas to take on cats which owners can't afford to take to the vets (or requests for money to pay their blinking vet bills! 
). I think that then, just as now, if they can't afford massive bills for a dog or cat who has suffered a major RTA, had cancer or what have you, they opted for put to sleep.
In the last 12 months alone my personal vet bills (not my rescue ones) have been over £6K, easily.
One (large breed, so costs of surgery even higher than small breed) dog had a suspected tumour removed and biopsied. Thankfully it was 'just' an internal infection, the other had surgery for ear problems (common in this large breed). I had no particular reason to suspect that these problems would occur, especially the dog with the fast growing internal lump, they just did.
My third large breed dog had treatment for cancer and another terminal illness and after many vet visits eventually we had to have him put to sleep a few months back - there was no kind option, we'd done all we could but he was beginning to suffer and there was no cure but I spent a fortune on giving him a few more months of love and quality of life. He had for years been on daily medication for epilepsy as well, costing about £600 a year alone. He had a pedigree a mile long and was KC registered, there was no known cause of the epilepsy, it just happened. How was anyone to know that the bouncy pup would in a few months need daily epilepsy medication for the next 12 years?
Two of our cats were ill, one with epilepsy as a result of past abuse, another with liver failure due to the same. Both were hospitalised, one on a drip and daily meds for months and stabilised for a few weeks then regressing so I had to call the vet out to the home on a Saturday night and let her go - nearly £200 for that visit alone. Our ferret was put on meds and had several vet trips and eventually we had to make the decision to let him go too as there was no further treatment which could help him.
Okay, we had a lot of pets and have had a shitty year of sadness and admittedly I knew the kittens were going to be vet bills on legs (that's why I took them in, because no-one else would give them a chance and they would have died in pain and suffering even earlier, without having known love and care) but even so the two dogs we still have alone cost us a small fortune just to keep them healthy and alive. I would have been in dire straits without insurance.
People look at their little puppy and think, "What could go wrong? but they don't think of the possibility of traffic accidents, grass seeds in the eye, swallowing things they shouldn't (pups are terrible for that, generally requiring surgery to remove the foreign object), congenital disease due to bad breeding which becomes apparent after a few months of being with the owner, breed related illness such as hip dysplacia in Labradors, for e.g.) or the later costs which come with age related illness.
A qualified dog behaviourist friend bought a Border Collie pup from a very reputable breeder, having in the past had rescue dogs. She'd never had a health problem with her rescues but for personal reasons wanted a pup she thought would be hers to train and who would have no issues to iron out from day one and she chose the breeder with so much care, personal recommendation from trusted and worthy sources and so much research that even her rescuer friends were begrudgingly impressed.
Her pup has Addisons disease. It became apparent when he was a few months old. He's been in the vets countless times, she's nearly lost him goodness knows how many times, he's been hospitalised and is now on lifelong and very expensive medication. Without insurance she would have decided to forgo renting a house and be living in her car with him now. Without insurance most other people would have kept the house and had the dog put to sleep.
Consider very carefully.
If you have a credit card or spare funds to cover, say, £4 or £5K of surgery tonight, should your dog break a limb or show sudden signs of something like Addisons or have a road accident, then you can rest comfortably knowing you can cope. If all you've got is a few hundred or so and can't raise the rest ask yourself what you'd do if one of those incidents happened tonight or tomorrow morning.
If you pay into an insurance policy then yes, it may be "money down the drain", but what price peace of mind? Will you look back and say, shit I could have gone to Florida, I didn't need to spend that on insurance or will you say, thank god I didn't risk it?
My insurance comes out by direct debit and I don't even think of it as my money, it's no more mine for shoes or holidays than the money in the bank for the monthly electric direct debit.
I use Purely Pets for dog insurance. They've paid without quibble and will bill the vet direct and not require you to pay first and claim it back afterwards. It costs me just over £40 per month for two large breed dogs, one over the age of 8 (where it gets more expensive no matter who you're with), one just under 8 years. Admittedly I pay the first £99 of the bill for any one course of treatment for the older of my 2 dogs but that's a standard excess with any pet policy. With the dog who is over 8 I pay on top of that first £99 the first 35% of the remaining bill but that again is common across the board of insurers and won't apply to you as an owner of a pup or young dog.
Both are breeds which have known problems with their back legs, hips and in one dog's case is a breed which has the highest chance of all breeds for suffering from a particularly horrible and incurable disease which needs a lot of management and medication. The policy also covers vet prescribed diet and vet prescribed vitamins and minerals which is important to me as the known likely illnesses are ones which require those things in order to give the dog the greatest chance of an extended and good quality of life before the effing disease takes over completely.
The kitten with epilepsy was insured with Pet Protect. That cost me £7 per month, they too paid without quibble and direct to the vet without me needing to pay first and reclaim. Her bills ran into thousands. Bluntly, without insurance I too may well have been looking at living in a car!
Unless you are affluent and can afford to find at least £5,000 on the spot or have a credit card that you will never use with that limit on it I really, really would recommend insurance. Only you know your finances, all I can say is please think carefully.