Yes he does. It is a heavily leveraged deal.
He needs to cut costs immediately and show profitable operations, then he can think about refinancing that debt.
Elon Musk is the new owner of Twitter Inc., ending months of uncertainty for Silicon Valley and shareholders. Yet for debt bankers on Wall Street, the drama is far from over, as they’ll need to convince investors that the Chief Twit’s ambitions for the company can justify its heavy debt load.
www.bloomberg.com
The thing is... You've made an argument that Musk himself isn't even making. He didn't even claim these firings were about productivity. He said the firings were because twitter isn't profitable. That is why he is cutting entire departments.