Who else could have done it?

L is not an INTP

Introverted thinking (Ti) is an introverted judging function; its job is to provide guiding principles that govern what to do with information and setting goals. As a thinking function these principles are based on logical information (rather than felt information). Ti cares a lot about correctness and accuracy - the Truth. i'll note here that whether L is INTP or INFJ he would still use Ti for guiding principles, the process is just prioritized a bit lower.

Extroverted intuition (Ne) is an extroverted perceiving function; its job is to be nonjudgmental and interested in exploring and engaging the world. As an intuition function, it deals with abstract information (rather than what can be observed with the five senses) - so, basically, it deals with hypotheticals. For Ne, anything is possible, and they'll consider a number of different scenarios and possibilities, altering different variables and "throwing things at the wall to see what sticks."

The Ti/Ne process is often associated with deductive reasoning. Ne throws everything at the wall, Ti observes what happens and draws conclusions based on what sticks. This is, I think, why a lot of people type L as INTP - for example, he's able to consider possibilities like "maybe Kira really is a god."

The problem is that in practice this is basically just not how L approaches the case at all. If someone primarily using Ti and Ne were running into situations like L did when Light lost his memories, he'd be wondering, "Was Light really framed?" before Light suggested it. Even when the logical information doesn't add up anymore - like Kira continuing to kill after Light had been in confinement for two weeks - L VERY NOTABLY stalls the case for months instead of trying anything new! L is not an INTP and everyone is soooooo annoyed with him because he's not.

2. L is an INFJ

Okay, so he's not engaging in the deductive reasoning process associated with INTP. What is L doing then? I'm glad you asked :)

Introverted intuition (Ni) is an introverted perceiving function; its job is to absorb and retain specific kinds of information that form a base view of how the world works. As an intuition function this worldview draws on abstract information - so basically, it deals with axiomatic assumptions about patterns the world conforms to (e.g. "justice will prevail"). Ni basically forms schemata and stereotypes about the world - for example, that a certain "kind of person" will act a certain way, based on the person's observations. those schemata form expectations and allow the person to analyze or make predictions.

Extraverted Feeling (Fe) is an extraverted judging function; its job is to present information to other people in ways that will affect and influence them. As a feeling function it seeks to influence people with emotional information (rather than logical information). Fe basically taps into the mood, sets a tone, and reads other people's feelings and desires. they tend to feel and be deeply affected by other people's feelings though they don't always show it.

Ni/Fe combines into an approach to the world that relies on reading other people, both emotionally and in terms of patterns about "how they are," and making predictions and assumptions based on long and deep observation of those people and of the world. they're attentive, focused, insightful, and piercingly perceptive.

this is how L actually deals with the Kira case. the moment Light makes a smartass comment about the fake tip that 1000 investigators were to be sent to Japan on camera, he piques L's interest because it flags to him that Light is a "certain kind of person." When Light loses his memories, his question to L is "Do I really seem like that kind of person?) (Light, as an INTJ, is also primarily using Ni, though he uses extraverted thinking instead of feeling). L understands the question and his response is "Yes you do, I've always thought so." He doesn't lay down a litany of reasons why he's tried this and that and it comes back to Light (he hasn't tried this and that lol...) - his judgment of Light is based on his assessment of Light's character.

Notably, L also gets some things wrong about Light because of these assumptions. He's convinced Light would kill his father because he thinks the type of person Light is would be ruthless. that's based on his HEAPS of experience as a detective - Light fits a certain archetypal profile that L has in his head. he's mostly right about Light because he has a very very solid base for the schemata he holds, but he sometimes gets things like that wrong bc Light doesn't perfectly conform to the stereotype.

L is a very excellent judge of character and he's able to read people emotionally. a lot of Light's efforts go toward neutralizing his own emotional expression but this actually makes L more suspicious of him bc L can tell it's insincere. the one time that L actually doubts Light might be Kira when he still has his memories is his outburst at the hospital. L reads that, judges it as sincere, and finds that it doesn't fit with his archetypal read of Kira, so he wonders if maybe he made a mistake. the actual problem in that instance is with his archetype not with his suspicion of Light. his suspicion of Light is primarily based on how he feels about him, the logical aspect is largely just support for that.

he's also able to reach others emotionally very effectively when he's up to it. he knows how to get the police force pumped and build their confidence, and when he's feeling like shit he makes everyone else feel like shit too lmao. he's also sensitive to other people's feelings even if he doesn't always cater to them - when people are frustrated or upset with him he gets depressed.