Its the other way around the weight of a mouse gives stability and the size gives more area to grasp which allows for more controlSo if I give you a chopsticks of 1km circumference, you'd be able to have more control over your food? Obviously not.
So if I give you a pentelpen and ask you to write your name of approximate 12mm standard font size, you'd be able to provide a satisfactory, hassle free result? Obviously not. Pentel pens are structured to discard control of where its ink will go with its increased ballpoint size compared to regular pens (ballpens, fountain pens etc.). Its purpose is just to mark which benefits more in size than precision that's why it's called a marker
I'll give you another clearer example just in case these already clear examples still isn't enough for you to stop with this false statement.
Write your name with a tablet pen in MSPaint.
Write your name with a mouse in MSPaint.
Just ignore the matter of speed for now, which among these two peripherals offered more control and ease? Which has better legibility?