Did she give you reasons?
Pump capacity depends on the pump. Anywhere from 200 units to 480 units.
Yes, you could set it to give you more insulin gradually.
With pumps you can basically set them up to deliver in any way you want.
Are you taking basal insulin also? Like Tresiba or Toujeo or Lantus?
If you are only using insulin with meals, I could see where a pump might not be as useful. But if you are doing basal, then a pump could be helpful for you.