In short, not all demand curves have a monopoly price point at which you would make more money by restricting supply (e.g. it's possible to have a demand curve where demand would fall off a cliff if price went up slightly, even if supply went to near-zero. in this case, you cannot make monopoly profits). And even if there is a monopoly price which could provide monopoly profits, it can be hard to figure out what it is and you can lose money (or even go out of business) trying to find it. Therefore, not all monopolies can lead to monopoly profits.

Quoting minimally:

http://mises.org/humanaction/chap16sec6.asp

> The special conditions and circumstances required for the emergence of monopoly prices and their catallactic features are:

> 1. There must prevail a monopoly of supply.

> 2. Either the monopolist is not in a position to discriminate among the buyers or he voluntarily abstains from such discrimination.[12]

> 3. The reaction of the buying public to the rise in prices beyond the potential competitive price, the fall in demand, is not such as to render the proceeds resulting from total sales at any price exceeding the competitive price smaller than total proceeds resulting from total sales at the competitive price.

> 4. It is a fundamental mistake to assume that there is a third category of prices which are neither monopoly prices nor competitive prices.

> 5. [some stuff about cartels]

> 6. The concept of competition does not include the requirement that there should be a multitude of competing units. [i think you will have to read further to understand this one]

> 7. If it is possible for the seller to increase his net proceeds by restricting sales and increasing the price of the units sold, there are usually several monopoly prices that satisfy this condition.

> 8. The monopolist does not know beforehand in what way the consumers will react to a rise in prices. He must resort to trial and error in his endeavors to find out whether the monopolized good can be sold to his advantage at any price exceeding the competitive price and, if this is so, which of various possible monopoly prices is the optimum monopoly price or one of the optimum monopoly prices. This is in practice much more difficult than the economist assumes when, in drawing demand curves, he ascribes perfect foresight to the monopolist. We must therefore list as a special condition required for the appearance of monopoly prices the monopolist's ability to discover such prices.

> 9. A special case is provided by the incomplete monopoly.

> 10. Duopoly and oligopoly are not special varieties of monopoly prices, but merely a variety of the methods applied for the establishment of a monopoly price.

> 11. The monopolized good by whose partial withholding from the market the monopoly prices are made to prevail can be either a good of the lowest order or a good of a higher order, a factor of production.

> 12. [discussion relating to governments intentionally encouraging monopoly]

And it goes on.

The biggest takeaway is that monopolies sometimes but not always enable higher profits by restricting supply. It's important not to assume all monopoly will enable significantly more profits than competitive market prices. Some analysis is required in any given case.

And the issue of whether and why monopoly prices are bad, and what if anything should be done about them, is considerably more complicated than "the government should prevent all monopolies" (typically with no mention of whether they are charging monopoly prices, or even could profitably do so tomorrow).