Short answer: Yes. Processing speed, fees, and investment returns all matter.
Yes. Different providers have different rules for how quickly they process withdrawals. Some let you withdraw online. Others need paper forms. The investment returns also matter because more money in KiwiSaver means less mortgage. Check fees and past returns, not just the withdrawal process.
Provider A: 3-day online withdrawal
Provider B: 2-week paper forms
Fee Difference: 0.5% per year
On30000 Balance: $150/year difference