If you have very few short rests that is.
You only get 1 back on a short rest.
But yes, more short rests helps the fighter more than the paladin.
But it also helps the monk more than the fighter.
Spiked growth is only exceptionally good if you allow rules exploits. Otherwise it is just good.
If you cast it directly on someone, they take 8d4, no save, and have to dash to get out (assuming 30' movement).
And that's before pushing.
Compared to a fireball with 8d6 with a save 4d6 on a save from a fireball. The same damage without slowing (also without concentration).
Paladin is great if you have many long rests. Also they are very bonus action dependent.
Second wind is also a bonus action.
Monks waste their reaction on deflect blows. So a fighter is more sticky.
The monk alread took an attack or 2. Don't need to be sticky if they already attacked.
At level 1 to 4, the fighter easily competes with both of them.
Things are much closer than 2014.
Also you should not forget, that the fighter mlst probably has way higher Con than a paladin
paladin gets 5hp per level with LoH.
Fighter gets 4hp per level with second wind, assuming one short rest. So even with +1Con, that's even.
But Cure wounds scales even faster than either one.
And they can much more easily fight at range than both Paladin and monk, even if they are mainly melee guys. Because they don't have 2 stats to keep up. Just a single one, STR OR DEX.
Monks don't need Str.
And a paladin can also go Dex. Nick is really nice with paladin 11, though that is out of scope.
Don't make the mistake to underestimate the fighter. They are very good at what the should be good at: fighting.
Everyone else is good at it too.