If I produce a product at a cost of $10 and sell it for $11, what happens if someone else figures out how to produce it for $5 and sell it for $6? I either figure out how to produce it cheaper or I go out of business. Either way competition has lowered both the cost and the price

You will also notice that the profit margin is the same in both scenarios ($1). So, if my competitor sells twice as many at $6 than I did at $11, he makes twice the profit that I did! So whose the greedy one?

Let's say instead the govt paid for my product no matter what the price and passed legislation that made it very difficult for new competitors to enter the market...

In that case, why would I worry so much about controlling costs? So maybe the cost to produce goes up to $15 and I sell it for $16 (or $116, who cares? The govt is guaranteed to pay for it)

If you want to know what is wrong with things like healthcare and higher education, a massive piece of the issue is govt interference with subsidies and stifled competition that have led to run away costs (little incentive to control them) which leads to higher prices.

More competition. Less government.