The OP doesn't actually propose giving the money as profit. An alternative interpretation of his proposal to "let people pay more" would be for the government

The OP doesn't actually propose giving the money as profit. An alternative interpretation of his proposal to "let people pay more" would be for the government to offer a prize to companies for producing X number of additional vaccines by a certain day, offering to buy them from the company for say 3x the current price - then selling a portion of those at 5x and giving the rest away for free to need people, to balance out the cost. This would be a truer test of "Do companies really, really not have any extra capacity? Or are they just allocating resources according to profit maximization, not to maximum effort?" This is what normal markets ARE - companies take risks and investments for a chance at profit. The government could fake the system by offering high rewards... or we could just let companies do reasonable things like sell 20% of their output at market price. This reminds me of the CCP in the 1950s where most private land was socialized... and farmers ended up putting all their effort into their private plots, because that was the only work they could do that they'd actually get to keep.