At the back, you'll only make the bike go faster by changing the smallest sprocket to an even smaller one.
As he has an 11 tooth small sprocket, he'd have to change it to a 10 tooth one.
This means changing to at least an 11 speed cassette with probably a whole new drive train.
At the front, it'll mean changing to bigger chainrings.
Depending on what's exactly on the front it could be as simple as just buying new bigger chainrings and a new chain and moving the front derailleur up a bit.
Or as complex as buying a whole new crankset with bigger rings with maybe a new bottom bracket, derailleur and chain to go with it plus then fitting them.
Hence the bike shop saying it may not be worth it.