Batch Sparging

Ive been away from my hobby for a while, and am starting back in slow with some extract batches. When i brewed all grain years ago i fly sparged.

Im building a Igloo Cooler HLT and MLT and plan on batch sparging. I am looking to use a pump to sparge. After the first runnings, how do you guys sparge? IS it ok to just pump the sparge water in through the outlet, since you are mixing up the grain bed anyways?

That's always how I've done it.

I use the igloo cooler and after i drain my first runnings I just pour my sparge water in the top. Then I stir it up and let it sit 10 minutes. This may not be right but it's simple and I'm hitting about 70 % efficiency which is good enough for me.

Looking to avoid having to mess around with another penetration in the cooler.....

I guess i'm confused. What's wrong with opening the lid to sparge. Everything is getting boiled after so no infection? Mash is over so all your doing is basically rinsing the grains. I'm fairly new to all grain myself so (1 year) so if this is bad can someone explain.