"Why can't the US military increase the pay for the soldiers, hire more soldiers and reduce the number of contractors?"
Soldiers aren't paid very much directly, but the indirect costs are huge, including at least room and board, training, and future benefits including medical care (via the VA system, currently almost $113 billion/year).
Quickly Googling for estimates of the cost gives answers between $350,000 and $400,000 per soldier per year.
So, to answer your question, we don't because it'd cost more.
Soldiers aren't paid very much directly, but the indirect costs are huge, including at least room and board, training, and future benefits including medical care (via the VA system, currently almost $113 billion/year).
Quickly Googling for estimates of the cost gives answers between $350,000 and $400,000 per soldier per year.
So, to answer your question, we don't because it'd cost more.