(Excessively) Regulated exchanges have major drawbacks, but at least investors have some amount of protection. Ideally, I strongly prefer free markets, but the early days (when there is a lack of trusted sites) can be very dangerous.
Hm, "free market" does not mean "unregulated market". A free market is one without significant obstacles to the entry of new suppliers, where suppliers can freely offer varieties of their products and fix their prices, and where consumers can freely choose among the available suppliers.
Regulations that protect customers are no problem, as long as they apply equally to all suppliers and do not effectively prevent the entry of new suppliers. It is still OK if the regulations prevent the entry of
certain suppliers, e.g. for being too small, foreign, unqualified, whatever The important point is that if the price of the product were to rise much above its cost, or the quality were not not as good as it could be, other entrepreneurs would promptly enter the market and offer the product at lower price and/or better quality. As long as this "liquidity of suppliers" exists, the market is free, and will eventually reach a "fair price" -- one that provides to each supplier about the same net revenue that he would get if he switched to some other activity.
In fact, strict regulation is essential to ensure that markets remain free. In an unregulated market, the suppliers that first dominate the market will inevitably try to use their positions to keep competition away, by any means they can. These include dumping to force smaller competitiors into bankruptcy, bribing the government to issue exclusive operating licenses, prohibiting retailers to offer products of their competitors, and many dirtier tricks. The market will then become a monopoly, or an oligopoly run by a cartel -- and prices will be set so as to maximize the suppliers' revenue, rather than at a fair value.
Regulations that protect customers also increase consumer confidence, and therefore are benefical for all suppliers in the long run. (We can see that in bitcoinland: people are being driven away from bitcoin by the fear of losing money in ventures and exchanges that they cannot trust.)
For this reason, many countries have things like anti-monopoly laws, anti-dumping laws, and consumer protection agencies that try to limit the market share of individual suppliers in order to keep the market free (although they rarely succeed in that goal), prevent scams, and impose quality standards. Honest suppliers may grumble at such regulations, but know that they are good for them too. Deregulation is mostly the demand of the myopic, opportunistic, or fraudulent supplier, who aims to make quick money in the short term, even at the cost of damaging the market in the long term.