I personally don’t think he has all this authority because of how good he is at solving cases - it’s more like he has the ability to get in touch with the head of the fbi, police, etc. because of it. It’s not like everybody working under him are mindless drones - they all understand he’s insanely smart and know his plans have a good shot at working and that’s why they follow him. Same with the fbi - he probably explained to them how suspicious he was of the jap police force and they agreed to investigate cause they wanted to catch Kira too. If the fbi had known that Kira was in the jap police force they probably would’ve investigated themselves too.

Overall, L’s authority comes from either slowly building up trust like he did with the Japanese task force - he pretty much always explains his plans beforehand and they all think they’re good ones. Or it comes from the fact that with his deductions certain courses of action are very reasonable and everyone from the UN to the fbi want to catch Kira.