Like many iconic Yu-Gi-Oh! cards, Effect Veiler made its first appearance in the anime, when Yusei Fudo used it to stop Lotten's (Eng. Lawton) one-card FTK deck. During Lotten’s Main Phase, Yusei discarded Effect Veiler from his hand to negate Gatling Ogre’s effect until the end of Lotten’s turn, giving him a chance of survival in their duel. This appearance could have been a foreshadowing as to where the TCG was headed. But back in 2010, one-card FTK decks were actually not very common. It was a slower time then, when stopping a single monster effect had a way bigger impact than it does today, like stopping key plays by Debris Dragon. Strangely, this card has been popping up again due to several niche aspects.
There are easy-to-spot things that separate Effect Veiler from other commonly played hand Traps. She (yes, she) is a Level 1 LIGHT Spellcaster Tuner, and all these attributes were probably relevant at different points in time. However, these are not what makes her great. The amount of different hand Traps that have seen play in only the past few years is more than you can count in one hand. There are overlaps and situations other Traps would not be able to tackle, so think of this as a Venn diagram. Its most comparable hand Trap would be Infinite Impermanence.
Infinite Impermanence, in contrast to Effect Veiler, can be used at the start of your own turn in order to halt floodgate-like effects, such as Thunder Dragon Colossus or Naturia Beast. Since Impermanence is an actual Trap card, it can also be Set and used later. Now this is exactly where Effect Veiler has found its niche in the format. Denko Sekka has been rapidly rising in popularity, and not even a set of Infinite Impermanence can clear that threat in order to unlock the rest of your back row.
While many effects can be countered by Ash Blossom & Joyous Spring, not all of them can. Some examples are Brotherhood of the Fire Fist - Tiger King, non-co-linked Knightmare monsters, Trickstar Lilybell, and Altergeist Marionetter. There are many more.
The polar opposite of Effect Veiler would be Ghost Ogre & Snow Rabbit. The former negates and doesn’t destroy, while the latter destroys and doesn’t negate. The decision on which one to run is largely dependent on what your deck can and can’t do, as well as which types of decks you’re expecting to go against.
Being nearly 10 years old, Effect Veiler has had 12 prints (as of 2018). Almost half are Common, and most are from preconstructed decks, namely Legendary Hero Decks (October 2018), Structure Deck: Powercode Link (August 2018), Starter Deck: Link Strike (July 2017), and Structure Deck: Synchron Extreme (August 2015). All are priced under 1,00 €, so you’ll probably pay less than 5,00 € for a full playset, making it only a fraction of the price of other hand Traps. It's a solid investment for new or budget players.
For duelists looking to add more bling to their deck, there are (pricier) alternatives as well. Ultra Rare copies from its first print in Duelist Revolution (2010) can easily be valued as 30,00 € for a playset, but the coveted Ultimate Rare print from the same set will cost you just that at a minimum for a single copy. But Ultimate Rare prints from that era look amazing, so it's a no-debate whether anyone would regret picking them up. During its 10-year lifespan, Effect Veiler has never lost its value to the metagame. It is safe to assume that it will continue to do so.