You can get coronavirus by breathing in cooties from an infected person. You can get coronavirus by touching stuff an infected person has touched and then picking your nose. But because disease spread is statistical, and because breathing involves one less step that touching, the CDC says transmission from surfaces is less likely to make you sick than transmission from airspace proximity:
The primary and most important mode of transmission for COVID-19 is through close contact from person-to-person. Based on data from lab studies on COVID-19 and what we know about similar respiratory diseases, it may be possible that a person can get COVID-19 by touching a surface or object that has the virus on it and then touching their own mouth, nose, or possibly their eyes, but this isn’t thought to be the main way the virus spreads [Centers for Disease Control and Prevention, press release, 2020.05.22].
A number of studies of flu, rhinovirus, coronavirus and other microbes have shown that respiratory illnesses, including the new coronavirus, can spread by touching contaminated surfaces, particularly in places like day care centers, offices and hospitals.
“What they’re saying is that high touch surfaces like railings and doorknobs, elevator buttons are not the primary driver of the infection in the United States,” said Erin Bromage, a comparative immunologist and biology professor at the University of Massachusetts, Dartmouth. “But it’s still a bad idea to touch your face. If someone who is infectious coughs on their hand and shakes your hand and you rub your eyes — yes, you’re infected. Someone’s drinking from a glass, and you pick it up near the rim and later rub your eyes or mouth, you’re infected” [Tara Parker-Pope, “What’s the Risk of Catching Coronavirus from a Surface?” New York Times, 2020.05.28].
Catching covid-19 and other respiratory diseases depends on increased levels of exposure. You’ll likely carry more coronavirus directly into your lungs from breathing in a confined space where an infected person is breathing or sneezing than you will from touching any surface in the same space and then expecting those cooties to make the long slog from your finger into your facial orifices and through your various mucous membranes down to where they do their damage.