You are correct in saying that "there are many other cards that search from the deck other monsters", but not every card allows you to do such for no cost at all and also for any lvl 4 or lower Warrior-type monster.
As you can see, the target cards for ROTA are many; at least 488 targets to be specific (according to my queries on the YuGiOh Pro database). This makes this card an extremely powerful option for many decks, and also a card with high abuse potential.
Now, speaking of abuse potential, doing some research I found that according to this official list ROTA card was brought down to the Limited status on November 2015, more than 2 years ago, and remains Limited since.
If we recall, the booster set Secrets of Eternity was released previously that year (on January), where the Nekroz Archetype made their debut appearance on the TCG. They were at that time perhaps the strongest Archetype out there, evidence of that is the Limiting of Shurit, Strategist of the Nekroz a few months later after their debut (on July 2015 to be specific).
Needles to say that Shurit is a Level 3 Warrior-type monster which basically allowed Nekroz players two things:
Use Shurit as the entire requirement to Ritual Summon any Nekroz Ritual Monster, and...
add any Warrior-type Nekroz Ritual Monster when doing so, or when tributing him in any other ways.
By having 3 Copies of ROTA in your deck you basically had 6 copies of Shurit, greatly increasing the chances of playing it.
Now, Limiting Shurit was not enough, as there was still abuse from Nekroz players. Specifically, regarding Nekroz of Clausolas which (guess what?) is also a lvl 3 Warrior-type monster that can do two things:
- Search for any Nekroz Ritual Spell/Trap card, or
- negate the effects, and make the Atk 0 of an opponent monster that was Special Summoned from the Extra Deck.
Not only is this card search-able by ROTA, but it also has the ability to do further searching ("thinning" your deck in the process, thus higher odds to pick the cards you want) and also negate effects like our good fellow Effect Veiler (hey they even look similar lol).
Bonus Fact: Other "searcher" spell cards have been Limited before, being Fire Formation - Tenki the most notable one, during the times of the Fire Fist and Bujin Archetypes. Again, had no cost at all, and even increased the Atk of Beast-warriors.
Given all these facts, we can say that ROTA was brought down with the advent of the Nekroz Archetype, which heavily benefited from its searching effect.
Instead of banning or limiting many cards from the Nekroz Archetype (thus killing it) they decided to restrict Reinforcement of the Army, the real source of abuse from this and other decks back then.