It makes the game more complex
This might seem like a minor point for a game as complex as Magic is. But this particular change introduces several different types of complexity in a way that is unhealthy for the game.
In order for Magic to stay healthy it requires a constant influx of new players. Magic has too many moving pieces for most new players to absorb it whole, so it's vital that new players be introduced to this complexity a little bit at a time.
Fortunately, Magic lends itself well to this sort of thing because almost all of the complexity is in card interactions, so players are naturally eased into the game as the pool of cards they encounter grows.
This free Lotus Petal that you propose violates that. It drops a one use only mana source onto the board at the start of every game. As game objects go it's no Ice Cauldron, but no Grizzly Bears either, and the very first object that a new player encounters in the game needs to be as simple as possible. (For example, right now, the first object most new players encounter is a basic land)
In 2011, Mark Rosewater wrote an article called New World Order
In it, he talks about how R&D came to realize that complexity was being introduced to new players too quickly.
He describes three types of complexity: comprehension complexity (how hard it is to understand what a card does), board complexity (how hard it is to understand the current state of the board), and strategic complexity (how hard it is to understand what you should do next).
The free Lotus Petal adds very little board complexity, and its comprehension complexity isn't particularly high either (although considering how many new players don't understand the relationship between mana and lands, I suspect it's still high enough to cause problems.) The big problem is strategic complexity.
For a new player with a simple deck, early strategy is simple. Choose to go first (if given the choice), play a land every turn, then play the most expensive card you can (unless it's obviously not useful). A new player with a simple deck can make it half a dozen turns into a game before needing to make a decision that isn't blindingly obvious.*
The Lotus Petal changes that. Do you play first or second? answer: It probably depends on what kind of deck you are playing. Do you pop the Lotus to pay for a 3 CMC card on turn 2, or a 5 CMC card on turn 4? answer: That depends on what you have in your hand.
A new player isn't equipped to answer these questions, and forcing them to have to deal with them at the beginning of every game is only going to frustrate them.
Even if the Lotus Petal improved the first/second player game balance, the added complexity it adds would harm the game more than the slight advantage first player gets.
*Savvy readers will notice that I left out the mulligan rule, which is technically the first complicated decision a player must make. But even that has pretty easy guidelines (3-4 lands or mulligan), and because one of the mulligan choices is "do nothing" it can be left out of early games entirely without significantly harming the teaching experience. The same is not true of the Lotus Petal which would need to be included in from the very beginning.