NO insurance policy is going to pay the whole cost of a vet visit. Generally you pay the entire cost up front and then file a claim and you get reimbursed for 80% of the "reasonable and customary" fees. What the insurance company considers reasonable and customary may be less than your vet actually charged if you live in most large cities.
To take your example of not being able to afford $300, you would still have to pay that to your vet up front (but with most vets you can use a credit card). Then file a claim. The insurance company might say that the R&C for what the vet did is $250. Then you would get a check from the insurance company for 80% of that or $200. So for your $10 a month, you get reimbursed $200 for your $300 vet bill. A fairly decent deal if you incur that expense within the first one year and eight months.
Of course, you could come up with any number of scenarios. Maybe your cat never gets sick or injured. But what if you have a $1500 vet bill? You could be insured for 10 years and still break even. Basically, when paying the insurance premium, the insurance company takes the gamble. Otherwise, you take it yourself.