Doesn't really exist around here. The closest you'll see is a cashier with no one in line going over to another lane to half-heartedly bag a few groceries. I am not sure what "parcel pick up" means -- there may or may not be a local analog.
Always ... but almost never in a situation where I don't know ahead of time that my car will be valet parked. A very few times valet service has been offered and I knew I didn't have cash to tip, I declined the parking service and parked myself. Fortunately, these were not situations where there was no other option but to use the valet service. All that said, my vehicle might get valet parked once or twice a year, maybe. Last time I used a valet parking service was March 2019, and I don't see another occasion on the horizon.
Agreed that cash can be helpful. A lot of the instances that it can be helpful, however, are heavily lifestyle dependent. Valet parking, for example, is not an everyday thing for almost everyone I know -- not even a monthly thing.