My tuppence worth:
A wider tyre will not necessarily offer any better traction/handling. In fact, because the side walls will be more squashed (bulging even!), it could make the tyre too flexible and work against you.
The only way to benefit is to have a wider rim as well.
And has been stated, is there room for this?
I suspect that the designers at Suzuki would have done the maths and concluded that the fitted wheel and tyre were the best for the bike design.
Of course, I stand to be corrected by the more erudite members...