There's thousands of troops of various countries already on the ground at Kabul Airport. However, the airport perimeter has been comprehensively breached and there's many people just milling around desperate to escape. Just look at the video of that C17 departing with people falling from it to their deaths. There is no way to operate aircraft safely there without re-establishing a secure perimeter and being prepared to defend that perimeter with significant force. That would not look great on TV.
I imagine that the best short-term solution would be to just let the situation settle and maintain the much smaller areas within the airport that are currently militarily secure.