I think I first started using synthetic oil in the early 1990s, when I was running a three-car fleet of '79 Civics. AAA Magazine brought to my attention the 10K longevity of synthetic.
But I'd never allow more than 4K miles before I changed the oil.
My mechanic -- who may want to sell me more oil changes -- noted that his father had changed his oil ever month or two. He didn't elaborate on his father's monthly mileage, even so.
Synthetic doesn't break down as fast as regular motor oil. The only reason not to use synthetic would arise from an oil leak that requires more than a quart every 1K miles. And if the car is burning oil, you have the prospects of an engine overhaul, failure to pass emissions, and the minor extra expense on oil as your immediate factors.
Personally, I wouldn't make much of a distinction between "10K" and "20k" synthetic formulations. If you change the oil and filter yourself, more frequent changes are an inconvenience. It's an inconvenience anyway if you take the car periodically to the mechanic for an oil change, and you might pay $80 for it. The advantage of longer lasting synthetic formulations only allows for less inconvenience and some chump-change savings.