Let's face it Minato was very irresponsible as Team Leader

[Simple Math]

he let Kakashi and his team go because Kakashi was a jounin.

 

[RasenUchihaChaos]

And btw:

He trusted kakashi as he was a jounin

Minato saw kakashi as a jounin, not as a kid

He wasn't like booohooo ur coming with me I'm gonna babysit you kakashiiii

then i guess he didnt know kakashi was the type to ditch teamates minato did the same thing as obito when he went after kushina