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Markets have to be resolved in order for participants to see the proper incentives to bet their actual beliefs.

If markets don't close, then those on the losing side have little incentive to sell their shares. The people with the right answer want to get their 100%, and will object to every micro-unit by which they have to compromise. It's also the case that those on the losing end have no incentive to close their bets out at all. They may even have abandoned their holdings, and can't be enticed back at any cost.

The markets have to be resolved.

The LMSR design requires a subsidy, and the calculations it uses to decide on prices always result in the AMM having enough funds to be able to trade. As the price gets arbitrarily close to 0 or 1, the market maker's funds get arbitrarily close to zero. If the market then swings the other way, the AMM collects money as the price moves back to the middle, so it can then subsidize trades again.

I'd like to see a design for a scoring rule that managed to increase B as the market gets thicker. The math for this is not obvious. It's not even clear what behavior would be desirable. It's possible to argue that since bookies collect a vig, it would be acceptable to charge more than the minimum on every trade, but every percentage the market takes makes it less likely for people to vote, and skews the market's output probability estimates ever so slightly.

I wouldn't mind talking about this more. (I'm the author of the explanation linked to above.)