This is wrong if you are saying that L's intuition is absolute. Even though he was accurate with predicting that Light is Kira, and he is said to have the "god's intuition" (not metaphorically, but rather hyperbolically),
it is still limited to only 90% confirmation. And again, L didn't know just then that Light was Kira, he still needed to attack Light and then have his intuition make his intuitive inferences.
Another thing which is funny is that L cannot run around and do his stuff, it is canonical that if L doesn't sit his usual way,
his reasoning abilities would drop by 40%, meaning that just when L tries to boost his reasoning, he would be perceived as weird and also his appearance is like that, meaning that a huge majority of NPCs would think of L being suspicious. Also, if this is not enough, he severely sucks at social skills, meaning that he will fail to explain a lot of stuff to others.
And while yes, L can go and burn someone just so, it will be too bad for him as well. Imagine you are in the middle of something, and you see a guy beating up someone just because they have an intuition which can have them be suspicious. L would be well-aware of that and wouldn't just believe his intuition. His intuition has good chances of being wrong and he is aware of that.
His best intuition feats are being 90% sure about Light being Kira from like Episode 5 and being able to "hear bells" about scenes before his unfortunate death.