No, even the stat boosts in Mario Kart Wii were ultra-annoying because everyone always played Funky Kong, Daisy, Baby Luigi and Baby Daisy, with some rare Warios and Bowser Jr.s (because they had the best stats, the ones that increased either the speed or the Mini-Turbo of your vehicle).
You'd always see the same characters every time, hearing the same exact voice clips over and over and seeing the same animations all the time, it was really boring.
The current method based on weight classed where no character has any stat boost outside of their class' stats is great, as it allows the characters to still kinda have an impact on your stats but it won't make one character be so prominent over the others (and even if Ludwig is indeed more played by other characters for his slightly smaller model which "shrinks" the kart a bit and allows to take curves in an even higher way, he's not as broken as any of the MKWii "top tiers", Funky would literally outrun you in a straight course section if you used the same vehicle and did the same actions but used a different character! It was so dumb! I can't even fathom how they added such a thing in the first place and THE EXTRA STATS WEEN'T EVEN DISPLAYED WHEN YOU PICK A VEHICLE!)
So yeah, having bonus weapons for each character would result in a similar situation where 1-2 characters have the best items and when playing Online you'll eventually get to a point where it's just those 2-3 characters repeated over and over because they're the strongest and everyone wants to use them to not be at a disadvantage. No, thank you, I want none of that...