Not if you consider door to door times.

(Obligatory "fuck cars and car-oriented developments" but to play devil's advocate here)

If driving: Most people's cars are parked in their garage/driveway, or on the street or in a group lot very near by. This means 0-1 minutes to get to the car. Snowy weather can add 1-10 minutes of cleaning/idling time, but since we're talking about a development in AZ I'm not going to count that here. There's the drive itself. Then there's finding parking (time required is very location-dependent, but since a grocery store was mentioned, those usually have huge dedicated lots that require 0-1 additional minutes to park). Then there's the walk from the parking spot to the store (again, for a typical US grocery store, that's about 1-2 minutes). So all in all, door to door times are only a few minutes longer than the drive itself, if that.

If taking transit: The typical numbers in American urban planning for a reasonable transit distance are 1/4 mi for a bus and 1/2 mi for a train. It takes 15-20 min for a healthy adult to walk one mile, but that doesn't include time to cross intersections (waiting for signal or gap in traffic). This will obviously vary wildly based on the route, 0-5 minutes depending. Doing some averaging math, you're looking at about 4 minutes to walk to a bus stop and 8 to a train, but up to 7 minutes bus and 15 minutes train (and I'm leaving out the time to get into the station because it varies wildly, but large stations can add several minutes just to get to the bus/train itself). Then there's the wait; you can reduce the wait at the stop by using an arrival app, but you still can't leave at exactly when you want like with a car, so I'm negating that benefit. Frequent service in the US is defined as anything from every 5-15 minutes depending on location and time of day, so average of 10 min, which gives an average wait time of 5 minutes. Then there's the ride: with only exception of the rare BRT, buses are always much slower than driving on account of all the stops and still being subject to the same traffic as cars. Trains fare somewhat better, although not streetcars, and many US trains follow interstates, where cars are traveling much faster than the train. So what might be a ten minute drive may be more like 15-20 minutes via transit. (Then there's a potential transfer if your destination doesn't happen to be along the transit route = more waiting and a potential longer travel time if driving would utilize a more direct route.) Then there's the walk from the bus/train to the destination, another 4-8 minutes. Taken together, door to door times via transit can easily end up being 2-3x longer than the trip itself (and many more times longer than driving the same route would have been).

So considering all factors, a "30 minute drive" will get you much farther and to many, many more places than a "30 minute transit trip." And while I used American figures, even "good" transit systems can be quite time consuming. When living in Tokyo (one of the best transit systems in the world where most people commute by transit) I lived very close to a subway that ran every 3-7 minutes and was a mere 15 minute ride before arriving at a stop quite near my work, but when all factors were considered (including a very long trek to/from the subway train through the station up to the street), my "15 minute train ride" was more like 45 minutes total.