Exploring can be helpful when it comes to grabbing certain hidden weapons (like the katana and submachine gun in Paradise Plaza) or stocking up on heals, but yeah. Early on, when you're a low level and Frank is slow, with a small inventory, running from one end of the mall to the other can cost you a lot of time. Otis telling you to trek across the map for a survivor is rough at the start. Using things like skateboards or the unlockable shortcut from Wonderland to Paradise helps a lot. There are some points in the story where the action stops and just lets you run around and do whatever, which is great, but most usually have at least one survivor to save or psychopath you can fight.
I like DR a lot, but it's one of those games where a lot of the difficulty is loaded up-front (Carlito's fights/The convicts/The gunstore owner/Early escorts) and the game gets easier as it goes along, rather than the reverse.