The fuse is there to protect the bikes wires and plugs from a overloading and over heating, Suzuki believed 3 amps was the maximum load that system should be put under.
Lighter sockets are not good at carrying a load and can very quickly get hot I would think that is why they went with a 3a fuse.
A 3a is perfect protection, going up to a 5a would allow you to put a greater load on the system than it was designed to handle.
The bigger the fuse the bigger the risk.
This happened to me.
My daughters car popped a 10a fuse, cause unknown, a new 10a fuse was put in place and away she went, a week later she had a fire under the dash.
I had to cut out and replace 66 wires under the dash then go back and find the cause, it was the numberplate light at the other end of the car.
You would think just swapping like for like would be OK but was not in this case.
Some of the 19 rides in my shed
2014 V2, Snoopy
2009 Wee, Pumbaa the pig
WR450F, The Blue Postie Bike
YZ250N smoker with rego, Stinky.
Yamaha MT09 (FZ09), The Scud missile.
Club Lead not Club Med.
He with the most toys wins.
Out of my depth in a puddle.
Live life on the edge you will see more that way.
Ridding a motorcycle keeps things in balance.
At the end of each trail and at the end of each day history is made.