The government has no money. So you're saying the tax payers should be paying $2000/mo/recipient.
In this scenario you've made nothing cheaper. You've only externalized the costs on to us. You could argue this is for my/public good, but you didn't ask me, you didn't get a representative vote from me. In your scenario you've just decided how to spend my money. I hope you understand you've only just made the problem worse because nothing has preventing it from being $4000/mo now that they know the gov will buy an unlimited supply.
edit: To be clear since posts below don't seem to get it... You're missing a step. You've done nothing to solve the $2000/mo problem, just shifted the costs to everyone. This is the issue with healthcare, the off the cuff solutions don't actually fix the root problems.