I assume they know the basics of gear adjustment, and would have corrected a limit screw adjustment, or bent hanger. So I'd suspect simple chain and/or sprocket wear.

There's no reason that you can't start in the gear of your choice, if your legs are willing to put up with it. But chains and sprockets wear over time, and if you spend the majority of your riding time in any gear it'll wear faster than if you spread the wear across multiple sprockets. That's especially true with the smallest cassette sprockets which have fewer teeth.

Chain wear is also highest on smallest sprockets because the chain has to flex through a greater angle as it winds on and off, plus the smaller the rear sprocket the greater chain tension compared to the amount of wheel torque (acceleration).

Start by checking your chain for stretch (pin wear), using a 12" ruler. If the pin to pin distance over 24 links is over 1/16" more than the theoretical 12" (24 x 1/2" pitch) your chain is worn. Given the fact that slips in high it's safe to assume the cassette is also toast.(yes you usually have to replace the entire cassette since loose sprockets are hard to come by).