It's a pretty important topic, and I was of the opinion that making a new one would cause the ideas hereto to be lost, which was something I didn't want to happen. ^_^

LV, as a mechanic of monsters that upgrade into higher forms, is something that I'd like to see developed on more, agree! The closest custom I've seen (outside of straight "LV" support) is the "Levelution" archetype, where the members were designed to flow into each other, but also had the ability to "add their LV". For example, you could tribute the Lv3 and Lv2 to "Level Up" into the Lv5. This introduces a lot more flexibility, and forms of "alternative progression" like this are something I'd like to see more!
Also, LV is fairly close to Ritual in terms of their weaknesses, but whereas Ritual requires you to have both Monster and Spell (and material), and both Monster and Spell are traditionally bricks on their own, all higher-Level LV monsters are traditionally straight-up bricks in all situations. As such, taking a note from Ritual and giving them alternative hand utility would be a good way to go about improving them!
Of course, one way to do this is to take a page directly from Nekroz and make the higher-Level monsters have Spell/Trap-like effects in the hand. The previously mentioned Levelution's big win condition Level 10 could be discarded to get the Lv1 (and since they couldn't LVUP to the GY easily, this served as a powerful design tool by making players run more copies so they'd always have one in Deck and could use the utility if they drew one- The exact opposite of how it's status("High-Level Brick") would have normally dictated its usage (to 1 copy).
An alternative was one I tried myself when I tried an LV archetype (sub-archetype?) where the higher-Level monsters had an inherent SS procedure to tribute their lower form, skipping the hoops of meeting your usual LVUP procedure in exchange for going -1 instead of +0 on the summon. This... could use some work since it kinda just upgraded them to the strength of Rituals without an anti-brick effect; Requiring 1 specific card on field and 1 specific card in hand. '^_^

Quickplay Pendulums can't exist, at least not in that way; Pendulums cannot be placed face-down by any circumstances, it's in the comprehensive rules. ;^_^

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(Pendulum Monsters) cannot be Set face-down, and you cannot replace a card in the Pendulum Zone with another Pendulum Monster.(裏側表示でのセットはできない。また、既にペンデュラムゾーンにあるカードを、墓地へ送って新たなペンデュラムモンスターに置き変える事はできない。)

That said, Pendulums that place themselves into Pendulum Zone from hand or GY or Extra with a certain trigger would be doable, and actually pretty interesting! >o<
Otherwise, make Pandemoniums. XD

While drawing vs searching is an important part of hand advantage, I feel there's one other trait we should also keep in mind- Hard Advantage vs Soft Advantage! ^_^
For anyone who might be unfamiliar with these concepts, Hard Advantage is when an effect truly pluses; The number of cards between your hand and field is greater than they were before you activated it. Soft Advantage is everything else; The quality of the cards between your hand and field has increased. As an example, a little graph I prepared:

"Dig" and "Fetch" can essentially be read as "Draw" and "Search"; I used somewhat more generic words so cards which gain hand advantage from the GY or like aren't accidentally excluded.

• Fetch effects give a deck consistency, giving the player access to combo pieces. They inherently increase the distance between a deck's skill floor and skill ceiling, rewarding players who know the deck, and how to use its tools. This is a very good thing, so it's very commonly seen in official designs.
• The examples of Dig in the graph are cards well-known for 'decreasing' your deck size, giving the player a better chance at getting to the cards they want in any given situation. While payoff is less guaranteed, the chance to draw into cards they can't search is very good, and decks such as "Zoodiac" often used these effects at the end of Fetch-focused comboes, gaining a higher chance of drawing into unsearchable Trap Cards, such as "Solemn Strike" and "Dimensional Barrier".
• Cards that grant Hard Hand Advantage lend their decks more longevity; Each additional card the player has is another backup plan for when a play gets shut down by Solemn Strike. These decks often end up coming out ahead in drawn-out games. Increasing the cards- and options- available, is powerful at any stage of the game, especially when your opponent starts falling behind in them.
• Most of the time, pure card advantage is a little too strong to throw around willy-nilly. Soft Advantage is useful for these situations, and often comes with the fun angle of how to make the numbers balance out! A good example is all of those "Discard 1 "x" card, draw 2 cards." spells (and "Darklord Ixchel"), and these often contribute another kind of soft advantage in addition to cycling less-useful cards, such as GY setup. A lot of open-ended potential here~

The cards I used on the graph are possibly the most boring entries for each category, to make explaining easy. For some more complex examples, "Graceful Charity" is both a +1 in Hard card advantage, as well as Digging 2 additional cards, and gives GY setup. The draw being first is also a useful contribution to its power (and banned status), as being able to choose the "worst 2" cards for your situation after looking at your random draws is very good. Dark World Dealings is a -1, but is similar in Digging 1 and bringing Soft Advantage.


But now, flipping the discussion totally on its head, I'll mention that this doesn't only apply to _positive_ advantage.

Had to use a monster for the top-right corner, since even early-days YGO was smart enough to not make a Spell/Trap with "Look at your opponent's hand, choose 2 cards from it, and <get rid of them>.". XD
As a big note, there are much less effects that minus your opponent's hand than those that plus your own. And those that do, do so to a much lesser degree than those that plus. This is largely because it's funner for both you and your opponent if you're both increasing your options, as compared to if you're decreasing eachother's options. Trims decision trees, makes the skill of the victim less relevant, etcetera. That's not to say negative hand advantage cards should never exist- "Nekroz of Trishula" and "Trickstar Reincarnation" are both good examples of cards in this category which are (on their own merits) balanced, if powerful, and the prevalence of Hand Traps can make this kind of effect very desirable. It's often wise to treat any effect as a +1 more than it would normally be. "More Mind Crush, less Delinquent Duo" is a good rule of thumb here. One effect I've tinkered with a a bit is "You can reveal 1 random card in your opponent's hand, then you can put that card on the bottom of their deck and make your opponent draw 1 card.", which would be close to the bottom of the totem pole, but due to being fairly low-impact in terms of general gain, it can be easily slapped onto almost anything with little worry of it getting out of hand, so it might be a good starting point if you want to play with this idea?


As far as where hand advantage can be gained from, the main examples would be Deck, GY, Banished, Field, and Face-up Extra, and where you're gaining from can drastically change how an effect is used. But I'll touch on that later, I'm kinda tired from rambling. '^_^