There are many reasons for this...
In 1e, the most a Fighter could get was three attacks in two rounds, plus one, if using a dagger or handaxe in the off-hand, for a total of two attacks per round... Nowadays, he gets that at 11th level, four attacks per round by 20th, plus an Attack of Opportunity (plus DEX more, with the Combat Reflexes Feat), PLUS up to three more, with Two-Weapon Fighting, Improved TWF, and Greater TWF.
Damage potential has also increased. From 1D8+6 for a Fighter with 18/00 STR in 1e, to 2D8+8 for a Half-Orc Fighter with a 20 STR getting a critical (and many weapons do better than 1D8), not to mention Power Attack, the two-handed damage bonus (improved still yet more by PA), and the many magical damage boosters...
I believe "To-Hit" bonuses also rise faster, but I may be wrong...
So there are LOTS of reasons why lower-level PCs have to rest and heal more often.
In 1e, the most a Fighter could get was three attacks in two rounds, plus one, if using a dagger or handaxe in the off-hand, for a total of two attacks per round... Nowadays, he gets that at 11th level, four attacks per round by 20th, plus an Attack of Opportunity (plus DEX more, with the Combat Reflexes Feat), PLUS up to three more, with Two-Weapon Fighting, Improved TWF, and Greater TWF.
Damage potential has also increased. From 1D8+6 for a Fighter with 18/00 STR in 1e, to 2D8+8 for a Half-Orc Fighter with a 20 STR getting a critical (and many weapons do better than 1D8), not to mention Power Attack, the two-handed damage bonus (improved still yet more by PA), and the many magical damage boosters...
I believe "To-Hit" bonuses also rise faster, but I may be wrong...
So there are LOTS of reasons why lower-level PCs have to rest and heal more often.