• This card is a good concept with a degenerate design.
• Has almost always been used in First Turn Kill decks (like Last Turn, Exodia, etc.)
• Has rarely if ever been used in competitive play in the 99% of other regular decks.

• It can be overpowered because you can use it's effect many times in one turn (draw 10+ cards from it)
• If you only draw 1 card from it, it will only be a 1 for 1 (barely worth the effort of using 3 Spells on)

• It is true that many decks don't have a high enough Spell Card count to maximize this card.
• However, even for decks with high Spell counts, there are reasons not to use it.
• Since it has 0 ATK and monsters need to be Summoned in Attack Position, it won't survive long

• A few years ago, they changed the rules so that the person who goes first has 5 instead of 6 cards.
• As a result, FTK decks are less stable and Royal Magical Library has little use.
  

Here's how I would've designed the card.

Royal Magical Library
LV4 LIGHT Spellcater 0 2000

When this card is Summoned, it is changed to Defense Position.  Each time a Spell Card is activated, 1 Spell Counter is placed on this card (max. 3).  You can remove 3 Spell Counters from "Royal Magical Library" to draw 1 card ; you can only use this effect of "Royal Magical Library" once per turn.

Anyway, as it stands my rating will be 1/5 (though at one point, it could've well been a 5)

Royal Magical Library
 
This card is most generally associated with OTK's, and actually the first time that I'd heard of it being actually useful was when Butterfly Dagger- Elma was legal. That, Gearfried the Iron Knight and Royal Magical Library could be used to OTK with Exodia.
 
Since then, Royal Magical Library is still consistently used in many Exodia Decks, was/ is used in Ignights and allows them to do quite a lot of "Stupid stuff" (to put it into a generalised way) and pops up in some Decks that want/ need to gain an early advantage in order to win.
 
Quite consistently, this card receives "Hate" due to the fact that apart from to assist/ enable OTK's or "Degeneracy," this card sees no actual play, and in all fairness, the "Hate" is actually quite deserved.
If this card was at 1 it would all but neuter its ability to be an effective "Abuse me" tool.
 
Arguably it might not totally deserve a Limit, but IMO, a Limit is probably deserved... 
 
Rating: 3. Generally this does nothing, but when it does do something it generally assists OTK or die Decks, and that really isn't what the game should be about.

Well here's an old card. Royal Magical Library is a Level 4 Light Spellcaster-type monster with 0 Atk and 2000 Def. 0 Atk is a big problem because that basically means that the opponent would be hitting directly. 2000 Def is nice, but this monster is rarely going to have the opportunity to go to defense mode. Level 4 is perfect for Summoner Monk. Light doesn't really matter because Honest's effect wouldn't protect it enough, and it becomes susceptible to anti Light cards (like yesterday's card). Spellcaster is good for Field Spells like Endymion, and Secret Village. The mixed bag of stats balance what can sometimes be a game ending effect. 
 
Royal Magical Library technically has two effects. The first is that it can store an unlimited amount of Spell Counters, one for every successfully activated Spell Card. It would be better if it was Spell effect because then continuous activations would trigger it, but that's not the end of the world. The problems arise if the Spell Card's activation is negated, because then you get no Spell effect and no Royal Magical Library effect. The second effect is what Royal Magical Library does with those Spell Counters. At the cost of removing three of them, a card can be drawn from the deck. There is no limit to how many times this can activate, and multiple Library's means multiple draws per turn. This is a good card if only because of how relevant it will always be to decks that need to draw. 
 
Score: 4/5 Good monster with past, present, and future potential. 
Art: 4/5 I'd want to see a book floating to one of the robed people. 
 
-WarlockBlitz

Royal Magical Library

The “enabler” of Yu-Gi-Oh. How I wish this card didn’t exist. For years and years, it has only been used in FTK’s, and it’s done its job well. I personally despite FTK’s and think little of people who use them in tournament play. It’s just an annoyance, and anything designed to win before an opponent can even use his cards is anathema to me.

But I digress. Outside of FTK’s, Royal Magical Library suffers from ATK deficiency. What I mean is that summoning this monster for the potential of his effect is just asking for a beatdown, and setting this monster does nothing for you. If Library had 2000 ATK and 0 DEF, it probably would have seen a lot more play over the year, even casual play. Many players know all about this card, but it is not a good monster, and I don’t think it ever really has been outside of FTK decks. But that’s why people know it. However, that doesn’t make the card famous… just infamous.

Advanced: 1/5

Future Potential: 1/5