They tried that with the early version of remake. It didn't go over well; in fact, it defeated the purpose of the remake system.
Players would merely five man one enemy in every match just to prevent remakes if the system allowed for that clause to be exploited.
And what of the 5 man team? What if one of theirs died just to prevent the 4 man to remake? That is to say, if the first blood didn't account for which side got it then a player could simply int one kill just to prevent remake and ensure their 5 man a victory.
So, no, no to all of what you just said. Congrats on you and your team accumulating 5 kills within 3 minutes though. But that sounds to me like someone on the enemy team was truly inting.
Let me ask you something. Would you like it if you were on a 4 man with 0 deaths, but couldn't remake simply because someone on your side spoon fed the enemy multiple early kills? Can you honestly tell me that you losing LP in that scenario is fair?