Foreword

Dragons, demons, devils and deities can all be terrifying enemies if your adventurers are caught half-beaten already. But for a prepared, intrepid and fully rested crew of adventureres it can make for some real bullying of even the greatest of foes.

The Troublesome Rest

The reasons for the creation of this alternate ruleset are motivated by the following reasons:

Pacing, if you are looking to run an adventure that has a longer timeframe, such as days, weeks or even months instead of the intended minutes, hours and days, the PHB rules fall short of giving a sense of resource scarcity over a longer period of time. This is especially true if you are looking to have a low-magic setting.

Balance, having an easy time resting means you have many resources to blast your way past obstacles. Either more or stronger hurdles must be employed if whittling down resources is sought.

Time, why spend precious time in a slog. Spending time overcoming many hurdles in order to drain resources takes a lot of out-of-game time. This can add to the experience, but not if the hurdles take up a significant portion of gameplay without adding to the experience.

The aforementioned reasons are especially at higher levels, where numerically the characters have more resources available.

Are These Rules for Me?

This ruleset is not for dungeon-delving gameplay. If your campaign is set around dungeons or adventures of similar pacing, I'd say to use the official rules on rests in the PHB (page 186) or the Gritty Realism in the DMG (page 267) if you're feeling hardcore.

This ruleset is for you if the aforementioned problems of pacing, balance and time are things you experience in your game.

These rules are only suggestions on how you may want to change the rules in order to make your game more enjoyable for your players. Feel free to modify them in any way you see fit in order to bring balance to your table.

Other Solutions

Here are a few worthy mentions that popped up when I posed this problem to the /r/DMAdvice on Reddit.

Adaptation of the world. Consider that the world is a living place and will change while the adventurers sleep. Enemies will many times adapt to the first incursion of their territory; placing traps, setting ambushes or making a preemptive attack on the adventurers while they are resting.

Pressed for time. You can always set a deadline. The necromancer summons his skeletal monster, the pirates sail from port or the evil regent legally acquires the kingdom are all good examples to push the adventurers to take action immediately.

Narrate the resting. "Make them [the players] feel like they are taking extra time to go set up a Long Rest each time. Narrate a bit of the set-up, the camp downtime activities, etc. This will only take you [the DM] 20-30 seconds or so, but it will ensure they feel time is passing." -ACBluto on Reddit

Waves of enemies. "Having 2 rounds or 2 minutes between dispatching one wave and dealing with the next won't matter too much, so long as they do not have time to rest up." -kendrone on Reddit

Embrace the big hurdle. "You'll be surprised what players are capable of against overwhelming odds. Not to mention if the party gets in over their heads with an encounter, then just let them retreat. Allow retreat to be a viable option. And if the party doesn't retreat then their TPK isn't on you, it's on them. Incorporate the TPK into the adventure. Maybe something like "One year goes by, darkness has settled into the land, the heroes of legend disappeared. (Talking to the same players with new characters) Your group seeks to take up the mantle of heroes to battle the encroaching darkness..."." -1D13 on Reddit

Note that none of these suggestions, including the following rules, are exclusive to each other, and can be used in any number of combinations to achieve a fun and balanced game.