From Greyhawk Grognard
«To wit, characters in a dungeon go through two or three rooms, find themselves down some hit points and/or spells, and then return to the surface, heal up and re-memorize spells to return on the next day. Or, alternatively, they barricade themselves in a room and camp out in the dungeon itself. It's a problem that especially presents itself in lower-level games, because the spell casters have few spells and must recharge more often.»
Whether this is a problem or not depends on your expectations. Frankly, given the high mortality rate of low level characters, it's surprising that they don't rest after every encounter (I ran a brief adventure in which this pretty much happened).
You can't blame the players. The game asks them to invest some emotional effort into customizing their characters. Players naturally do not want to throw that away early in a campaign.
If the DM allows for quick PC replacement of expired characters, the game loses a lot of its frisson. D&D isn't Donkey Kong.
The suggestion of the article linked above is to make the monsters more wary of PC incursions. That is exactly the recommendation found in The Keep on the Borderlands.
The essence of RPGs (and most other games) is the fallout from player choices. Sometimes a rapid, unyielding assault is the best tactical decision. However, this is rarely the case for low-level characters.
My own preference is to allow the party to rest whenever and wherever they choose and to put the monsters on guard (if warranted). For example, an aborted assault on a liar of orcs will cause them to post more guards and even create new traps at the entrance. A dragon who repels invaders will not be caught napping a second time. On the other hand, a tomb filled with zombies, skeletons and wights will not change their behavior once the party is out of sight.
Also, I see no harm in starting out the party with several potions of healing. That at least gets them through one extra encounter before a rest.
If you feel like giving potions for free to a party is "Monty Hall," then simply have the potions expire in a week and make them have no resell value.