Why do we use different micropipette tips for different volumes?
The short answer is yes, the accuracy is affected.

Automatic pipettes are most accurate in the middle of their range. The average error on a pipettes is already about 2%, but this is worse at the top end or bottom end of the pipettes minimal and maximal volume.

More subtly, have you ever tried to pipette 1 uL with a 1 mL pipette? Or even 5 uL. The bore of the pipette is too wide for starters, and the expulsion force/pressure to eject the fluid wouldn’t work very well.

On top of that, the surface tension would seriously hamper any ability to actually manipulate the fluid.