I've actually noticed that, no, you cannot rest all the time. My game crashed before I had a chance of saving, but after doing 'Investigate the Beach' near Silvanus' Grove I tried to do a quick rest before actually talking to the tiefling child at the beach - because I had had the encounter previously without all my spells available - and when I came back I found that the quest had gone about its way and the harpies had killed the boy before I could intervene. The world will progress if you take a rest, basically. That being said - because I have been playing 3.5 and 5e for a while now - I was used to making use of my cantrips more often than anything else and bringing out the big spells for tough enemies or groups of weak enemies. But even then my cantrips were doing work - as they should be. Eldritch Blast, Ray of Frost, and Firebolt were all getting used frequently by my warlock and Gale - EB because it's a warlock's bread and butter, Ray of Frost to knock enemies prone occasionally, and Firebolt to set enemies on fire.
Really, the only spells I was making over-use of were Shadowheart's healing spells, because I'm bad about using food. Also, too often when I'd use Help to pick an ally up they'd immediately be dropped by an enemy again - but that's a different complaint.