Gritty Realism is only situationally disadvantageous to dungeon crawling.
The drawback of slower recovery relies on an assumption, common to earlier editions of D&D, that the players will naturally undertake multiple combat encounters in one day.
My personal experience is that players are instead highly motivated to rest and recover to the maximum whenever possible, to protect the characters they've invested so much time into. If long resting now takes 7 days, the players will just rest for seven days.
However, there are some 5e game mechanics where danger triggers based on time or resources are limited by time, rather than by party actions like the decision to press forward or the schedule of long rests. These increase risk under Gritty Realism.
The primary risk factors are as follows:
- The DM actually enforces the standard rules on carrying sufficient provisions
- The DM uses random dungeon encounters
- The DM is running an adventure with a time limit
- The party uses spells like animate dead with a 24-hour duration
- The party encounters enemies with poison or disease
- Supplies are the primary limiting factor to how long you can remain in the dungeon without returning to civilization.
- Random encounter rate, set by the individual DM, determines the feasibility of resting in a dungeon.
- If the DM allows players to rest without cost or consequence, the extra resting time has no consequence. Gritty Realism would still be mildly more dangerous due to disease and poison effects and a few less feasible spells.
- City-based adventures, mysteries and intrigues, which don't try the four-or-five combat encounters per day gameplay mode of the dungeon, aren't so heavily constrained by the long rest schedule or ready availability of food and drink.
Supplies vs encumbrance
While most DMs I know don't strictly track food supplies and encumbrance, they are standard rules, and a DM using Gritty Realism might well use them. They can severely limit the amount of time you can stay in a dungeon.
According to Player's Handbook p. 185, a character needs a pound of food per day and at least a gallon (8 pints) of water. In fact, according to the equipment list on p.150, a day's rations weighs 2 lbs and a full 4-pint waterskin weighs 5 lbs. This means a character must carry 42 lbs of food for each long rest they intend to spend in the dungeon.
A character with Strength 10 can only carry 150 lbs, meaning that they can only realistically carry enough for two, maybe three long rests in the dungeon. Under the more realistic variant encumbrance rules, one long rest's worth of rations is nearly enough to encumber them. Not every party has a bag of holding, particularly at low level.
The spell create food and water only creates food which lasts 24 hours, and goodberry only lasts 24 hours. Neither of these are ritual spells. Gritty realism limits your ability to use this to survive a long rest.
You can leave and re-enter the dungeon, staying in hotels for weeks between fights, but exit and entry may be dangerous due to terrain. You'd also have to assume that the dungeon remains static in this time: no monsters repopulate, nobody else loots the dungeon while you're away.
Depending on how the DM chooses to run random encounters, the frequency of random encounters could make time spent in the dungeon more dangerous.
Dungeon Master's Guide, p.86:
You decide when a random encounter happens, or you roll. Consider checking for a random encounter once every hour, once every 4 to 8 hours, or once during the day and once during a long rest—whatever makes sense based on how active the area is.
Even if the DM rolls every 8 hours for a long rest period of seven days, that's 21 rolls at 15% chance per roll, resulting in a high likelihood. You can't risk a long rest so easily.
Dungeon Master's Guide, p.80, Twists, shows this optional adventure twist on its 1d10 chart:
The adventurers have a time limit.
Page 81 also describes adventure objectives where the player characters may face a time limit, such as trying to stop a ritual.
Poison and disease
Some poisons and diseases (Dungeon Master's Guide p.256-258) trigger based on time, rather than rest schedule. For example, recovery from Cackle Fever is timed based on long rests, rather than days.
Certain spell durations
Some spells have a duration of 24 hours. Normally, one can long-rest every day and maintain such a spell more or less continuously, but when a long rest is 7 days, this isn't possible.
Spells where this is a problem include animate dead, bestow curse, create undead, the banishing effect of divine word, druidcraft, goodberry, guards and wards, hallucinatory terrain, heroes' feast, mass suggestion, mind blank, Mordenkainen's magnificent mansion, Mordenkainen's private sanctum, Nystul's magic aura, telepathy, and water breathing.
Why is dungeon crawling the more dangerous than other activities?
Fundamentally, the dungeon is a combat-dense mode of play.
Chapter 3 of the Dungeon Master's Guide identifies four primary types of adventures: location-based, event-based, mysteries, and intrigue. Of these, location-based involve the highest density of encounters, meaning that you cannot plausibly go far before finding another combat encounter, or stay still without a combat encounter finding you.
But even comparing the two main types of location-based, which are dungeons and wilderness respectively, the dungeon is more deadly of the two due to two defining factors of a dungeon: its exceptional encounter site density, and the limitation of paths of movement between those encounter sites.
Dungeon Master's Guide p.99 describes the second of these traits as particular to the dungeon:
Within a dungeon, adventurers are constrainted by the walls and doors around them, but in the wilderness, adventurers can travel in almost any direction they please.
This means, for example, that if you had to climb down a cliff face and cross a risky lava flow to get halfway through the dungeon, you have to overcome these challenges again every time you try to leave.
Compare this to a wilderness encounter. Quite often, even if the woods are full of orcs, you can sneak past the orcs. You can make alternate routes through the woods, stealth your way through at reduced travel speed, and generally avoid many wandering monsters. You're likely to encounter fewer monsters than in a dungeon, due to the decreased density. You can literally lay low in the woods just by staying still, but you can't do this in a room in a dense dungeon.
Moreover, in most forms of wilderness terrain, one can hunt for food, and therefore survive off the land indefinitely. You don't have the problem of running out of supplies.