[RPG] Are there alternative ways to gain XP

As you say, this house rule works well for your group. A new player objecting to a house rule they don't understand is no reason for you to change it.

And they don't understand the point of the house rule. They've observed their fellow players and seen the rule's results, and are trying to adjust their actions to fit what the rule is meant to encourage — and they've misunderstood. Instead of engaging in new, creative roleplaying, they're just copying what they see other players do in a kind of cargo cult roleplaying.

This is also the source of their frustration: they think they've solved the puzzle, and they perceive you denying them the reward for solving it. They haven't understood it though, and rewarding them for missing the point will not help them integrate into your group.

Having put in effort and missed the "target" of understanding the point of the bonus experience, though, you should meet them halfway:

"It's clever how you noticed what the other players did to earn the bonus experience. That's great, but it's only halfway to getting the point of the bonus. The bonus is a reward for individual creativity in roleplaying, so simple copying doesn't earn the bonus.

"Does that make sense? This is an important tool that has worked for us, and I want you to understand what it's for so that it works for you too."

You need to emphasise that you're willing to help the new player get up to speed with the group. Emphasise that, because that's what the conversation should be about — not about whether the rule is useful or not (you already know it is for your group), and not whether the player gets to challenge the award (that's not their job in the group dynamic). Just take it as given that this is how it works, that's not up for discussion and don't bring it up for discussion. Move past those givens without even mentioning them, and instead move right to discussing with the player the point of it and how they can reach that point.

P.S. — Contrary to recent online RPG community fashions that resist XP rewards, this is a common and widespread way for RPGs and groups to work, and entirely functional when done fairly and impartially. Current fashion is simply that — passing fashion. Fashion is not legit grounds to tell you it's a bad way to run your game.

Don't punish your players for doing well.

A player having a +9 to Perception at an early level really isn't a problem. Sure, starting at level 1 with a 20 in Wisdom and Expertise in Perception is a little minmax-y, but that isn't an issue. The player obviously geared the character towards it, and punishing them by reducing their stats would be incredibly unfair to them, and punishing the rest of the group by making perception checks that are impossible for them unless one player gets lucky is just as unfair.

So, what can you do?

Don't rely on failing Perception checks to make an interesting dungeon.

The secret door? Now it's a magical door. They don't need to roll to see it; instead, they need to determine how to open it.

A tripwire trap? Nope; now it's a giant purple crystal that explodes if the players make too much noise. Instead of rolling to see it, now they have to figure out a way to get the party around it without dying.

An ambush of enemies? Now it's a group of enemies so large or fierce that the party decides they need to avoid the group rather than spot them and kill them.

You can even keep your usual traps, and instead add things in to make them something that requires an approach other than Perception. Keep the tripwire trap, but now the room is covered in magical darkness so they have to dispel that first. Keep the ambush, but now it takes place in an area with heavy fog, so Perception is at disadvantage.

That said, you shouldn't take away success from this player. It would be very un-fun, for both this player and the party, if you took away all Perception checks. She should have situations in which there is an invisible item to spot, or a trap that can be seen. Players have fun when they get to feel cool, and if they've geared themselves towards a large bonus in a skill, let them use it and give them that cool feeling.