To use conventional or run synthetic depends on the engine condition, driving conditions, and personal preference. If you are sticking to a relatively short oil change interval (3000 miles or 5000 miles) - I see no hard reason to run synthetic unless you see a wide range of extreme temperatures, run the engine excessively hard, or forgetful of oil changes.
An oil change interval of 25K miles on synthetic oil is possible - as long as you can control the amount of insoluables (usually means changed the filter a couple of times during the interval). Truckers have advance oil filtration systems (bypass) and can routinely run 10K+ miles on an oil change easily. With periodic oil filter changes - 100K+ oil service life is not unheard of.
But for a conventional car - daily driven. Up to you to pick the oil. If you are interested in running an extended oil change interval - then synthetic oil is the way to go. If you change the oil routinely at shorter intervals (3K-5K) - wouldn't make much financial sense to run synthetic. As with any extended oil change program - can't just blindly extend the oil change interval, even with synthetic. You have to pull used oil samples to be tested periodically, to see what the wear levels are and what the engine is doing. From those tests, you can see how much protection the oil has. For a clean, well maintained, modern engine - you'd be surprised on how long it can run on quality oil.
Myself - I run 7500-10K mile oil change intervals with synthetic. Given the amount of miles that I can accumulate - this makes the most sense for me, time and money wise. I pull UOA periodically to see what the engines are doing and to avoid any potential surprises. Opened up the engines from time to time - clean as a can be. Maybe once I get my Corolla up to 300K miles (@~225K now), I'll see some wear.
Doesn't mean that conventional motor oil is inferior. In fact, the current formulation of conventional motor oil now is almost as good, sometimes better, than a few older formulations of synthetic motor oil. If synthetic motor oils disappeared tomorrow - I'd have no issue running a conventional motor oil on a 7500 mile interval in my engine.
Sounds like the shop is trying to squeeze more money out of their customers, given that synthetics are significantly more expensive. Bottom line - run what you want, the key is matching the oil change interval with the protection level that the oil gives you.