How long would Death Note be if Light was actually a completely law-abiding, if vaguely narcissistic, citizen during the kira murders who just so happened to tick off L's "he's a serial killer" radar?
I mean, that's the thing, he wouldn't tick off L's radar
Why Did L Suspect Light Anyway
L does single-mindedly pursue the theory of "Light Yagami is Kira" to an utterly insane degree, even accepting for things like "he conveniently got amnesia for no reason" and "even though I put cameras in every corner of his house I didn't catch him" and "even though I handcuffed him literally to my side I couldn't catch him"
However, I will give L credit, he didn't pick Light out of a hat.
L's initial theory was simply that Kira was in Japan and taking a stab in the dark probably the Kanto region. Light confirmed this for him due to an egotistical hissy fit with L having to put in very little effort.
This brought L to focus on Tokyo.
L further figures out fairly early on that Light has a student's schedule, not a working adult's in Japan, and this is because Light at the time didn't realize he could control the exact time at which a person dies and by the time Light changes his method it's already too late.
Now, what happened then is that Light intentionally tipped his hand. After Lind L. Taylor, Light took L's existence extremely personally and nursed quite the grudge and the vendetta. To "win" as Kira, to prove he's a god to himself and the populace, he must personally kill L. As a result, Light does many things that put him in danger/do nothing to help him as Kira just to have his chance at L.
The big one is that he starts using information only known to the Japanese police force. He intentionally does this so that L focuses enough on Tokyo and the police there that Light can get a firmer grasp on him, what Light didn't account for was that L would immediately narrow in on him and him alone or the lengths he'd go to in order to investigate Light as a suspect.
But thanks to Light, L did know that whoever was doing this had access to police information not available to the public. Now, Light was likely hoping L would assume it was a cop, but L expanded his search to the police and their family members, presuming that family members may have access to these networks due to insecure home practices and such (which Light does).
Now, L never explains canonically why he's so certain Light is Kira, but if I'm putting myself in his shoes I can take a wager as to why Light made him go "ding ding ding".
L's looking for the type of person who would become Kira. He already knows this person is Japanese, likely a student in a rigidly structured school day (so not in university), but someone with good enough English to have followed the Lind L. Taylor broadcast, someone savvy with the internet so as to kill international criminals.
What he also knows is that Kira is obsessive, manic, single-minded, and unquestioning of his beliefs. Kira is also someone with an absurd amount of faith in law enforcement and the justice system (Light... doesn't spend too long questioning whether or not the people he sentences to death are guilty of the crimes they were sentenced for/the life circumstances which might lead to someone committing a heinous crime and whether or not that matters) which makes sense for a workaholic policeman's son in homicide whose son idolizes him.
Not to mention that, aside from his hatred of L, Kira is extremely respectful of the police in general. He never goes after the Japanese police the way he does L (only the FBI agents tailing him) and it's clear that his great rivalry is with L, not the Japanese police, interpol, or any kind of cops.
So, we're looking at someone who really respects the law... without understanding what the law even is, why it exists, or why "no, Light, murdering thousands of people does not magically make you exempt".
Adults typically don't act like Light does. Even after the six-year time skip, Light's still obsessive but he has changed greatly from the boy he was. And Mikami, an adult who is inspired by him and kills in the same way is... a very different kind of person ultimately driven by a victim mentality.
My point is, it would make sense for L to suspect a teenager rather than an independent adult. The schedule lines up, the personality lines up, and while this is very likely a highly precocious individual (and someone who knows he's very clever) they still feel young.
So, L narrows it down to a set of families and look what we have: Light Yagami, brilliant young man who scores first in the country on every exam he ever takes, talented in athletics at a national level, has succeeded at everything in his life and is the pride and joy of his family, utterly adores his police chief father and has repeatedly shown interest in following his career path and even taken steps towards doing so as a high school student.
But Back to Your Question
Putting aside whether or not anyone else would ever go as ham killing the types of people Light did for no particular reason (Misa, for example, would probably have only gone after her parent's killer. Mikami would have gone after his childhood tormentors/his mother. Higuchi went after corporate rivals) there's also whether they'd have that police information from Japan (probably not likely), and if they'd act the way that Light did.
Basically, while it is a nice thought... I don't think L would suspect Light in these circumstances as he'd ultimately be dealing with a very different person who acts in very different ways.
Light would never tip off his radar.