Isn't that what clerics were for? Get into that fight at first level, take a hit or two, get a cure light from the cleric. Job's a good'un. Our group is playing in a DnD Basic game right now, and we have yet to use a 5 minute work day, even though the Elf only has one spell, and we have no cleric (well, an NPC who we kicked from the party because he was making every single undead encounter meaningless).
Earlier games (pre 3.0?) had most of the class abilities, except spells, at will, or passive, or some ribbon bonuses for particular situations (Ranger preferred enemy). Everything else - fighting, thief abilities, ranger abilities, turn undead, etc. - were all "as often as you wanted".
Now, though, there is more "power" and more utility in the plethora of abilities/spell like abilities, and powers given by class, subclass, multiclass, feat, background, whatever, that many of them can't work in the current paradigm as "at will" type stuff. So they get tied to a recharge or rest mechanic, and players have been trained or decided that they need to have everything at their disposal of there is no chance of winning or no reason to press on. As mentioned, a lot of it is party dynamics, DM skill, and varies from table to table. But I have found the need for "rests" is waaay more now in 5e than in the Basic and 2e games I'm playing in currently. So, all IME/IMO/YMMV.