Is perfect competition always a more desirable market structure than a monopoly?

Perfect competition is a largely theoretical market structure, were there are a high concentration of firms in the market, who produce homogenous products and are price takers because if they increase the price, consumers will shop elsewhere due to there being perfect information in the market. Examples of a perfect competition structure are agricultural markets such as the producers of potatoes. On the other hand, a monopoly is a market structure with just one firm, which faces a downward sloping demand curve and is a price maker because as they have no other competitors the demand curve is inelastic meaning an increase in price won’t have much impact of the quantity sold.Arguably, perfect competition is a more efficient market structure, due to the perfectly elastic demand curve as well as companies in a perfect competition structure producing at their lowest cost as MC=AC. Assuming that the goal of both firms is to profit maximise, we assume that they are producing at the level where MC=MR. Allocative efficiency is achieved at point where MC=AR, which is where there is an optimal distribution of goods and services taking into account consumer preferences. Conversely, a monopoly which has no competition is not producing at its lowest average cost and is not being allocative efficient thus causing it to have abnormal profits as the AR is greater than AC. This is not efficient as they could be producing at a lower cost and making more of a product at a lower price. This causes a deadweight loss to society as if they produce more then all you want the product would be getting the product like in a perfectly competitive market.However a monopoly could be more efficient than a firm in perfect competition. The main reason here is the ability of a monopolist to make abnormal profits in the long-run, due to high barriers of entry to monopolistic markets. These profits can be invested in innovation of a product, which is ultimately more beneficial for all stakeholders in the market than the perfect competition model, which offers little prospect for innovation. Monopolies can also benefit from economics of size that perfect competition as they can reduce average costs by spreading costs over a larger output. Overall, it is clear that there are both, positives and negatives to these two market structures and each one suits better different markets.However, it seems that there is more potential for a development of any market in a monopoly, provided, however, that it is regulated by the government.