simple it reduces competition. if you were a member of an exchange would you want everyone in the world to be able to make markets or just your fellow members.
I don't know much about market making at CME, but I did research NASDAQs systems a year ago for a Level II based system. The thing about being a Market Maker with NASDAQ is that there are lots of rules and interface issues. There are pre-opening and pre-closing rounds of requests for On-Market-Imbalance orders based on simulated trading of the pending order book. When a market maker updates their quotes, this can trigger market crossing notification which must be responded to within so many seconds. It isn't just a question of being allowed to have two limit orders in place. I am sure that none of the retail products available at set-up to handle these special communications.
At one time, NASDAQ Options stated explicitly in their documentation that anyone could post a bid and offer simultaneously in the same contract. I'm not sure whether this is still true and I've never actually tried it. I'd assumed that IB doesn't allow it for any exchange (including ones that allow it) because they don't want customers competing with their Timber Hill unit, which is where the lion's share of their profit used to come from, although that may not be true anymore due to the intense competition in the "HFT" space.
If you place an order at a price that is better than the NBBO, often other MM's will join you at that price. This leads to a chance to manipulate markets, which can get you in trouble with the regulators. Let's say you have 10 CYH options - which typically have a large spread and are difficult to fill at any price other than the opposing bid/ask - and the current market is $1.50x$2.00. If you try to sell at $1.80 or $1.70 or even $1.60, you won't get filled. But if you place an order to buy 1 at $1.80, other MM's will join that bid and there may now be 10 or 20 bid at $1.80. You could now sell your 10 at $1.80 (if it were allowed, which it's not). People here have written in the past about how they used two brokers to do things like this and still got caught. Seems to me that it's not worth the potential legal problems to do this.
If this is in fact true... There is exactly ONE reason... And that is to maintain artificially large spreads... In order to exploit idiots who trade into these spreads. I find it hard to believe this is legal... But then Chicago more corrupt than Lagos. This kind of thing is unheard of in stocks... I'm on both sides on 100 stocks all day long.