I am also one of those who sees no value in paying for an annual service. Change the filter regularly, keep the outside unit clean, and pour vinegar followed by hot water down the condensate pipe every couple of months. Listen for strange noises, etc.
I googled "Should you pay for annual air conditioner service". Almost every link was for a service company warning that a costly repair awaits anyone who does not pay them to come out once a year. Here is the one neutral opinion that I could find.
When to Service Your Home Air Conditioner | Home Matters | AHS