I was a bit shocked when I found out that, when betting on horses, if you make a bet when the odds are 7-2, and a bunch more people make that bet after you did, you can be stuck with a bet at 5-2 odds;* the odds quoted before bets close is not really a price at which an offer is being made, so much as what in certain finance contexts would be called an "indicative price", that provides a certain amount of information.
The biggest — by far — justification I can see for a parimutuel system is that it's the 1930's and nobody has ever heard of a computer†; rather than keep track of who bet what at what price, you just keep track of how much was bet on Runs For Miles and take (most of) the money that was bet and prorate it. There's less bookkeeping to be done than if you're making bets on different terms with different gamblers, as is done with most Vegas sports betting, and there's no chance whatsoever that the house loses money; if it puts out 7-2 odds and gets a lot of bets, it doesn't just move the odds of future bets to 5-2 to try to attract bets to other horses, it moves the past bets to 5-2,‡ in some sense devaluing their weight on the book.
The context in which stock exchanges provide an "indicative price" resembles horse gambling in that everyone is placing orders and they are being accumulated without any actual trades taking place; a single auction is ultimately held based on the orders accumulated. Some of the orders will be limit orders — "Buy at up to $45 per share" — and others will be market orders — "Buy at any price." When the auction actually goes off, a price is determined at which the amount bought will equal the amount sold; if you pick a particular price and there would be more buyers than sellers at that price, you can drop the price until some of the limit orders to buy becomes active and some of the limit orders to sell becomes inactive, decreasing the number of effective buy orders and increasing the number of effective sell orders. Before the auction has executed — while they're still be accumulated — an "indicative price" will be quoted, telling traders what price the auction would obtain if no more orders were placed (or, alternately, if all future orders were balanced at that price); if you place a limit order at that price, though, and it moves against you, your order won't be executed.
With the proliferation of computers to facilitate the process, I wonder whether potential horse gamblers would be interested in a system in which you could place limit orders. Current horse gamblers are presumably selected for people who don't loath the current system with a burning fire of rage, but I think at the very least that "let me out if it goes past 3-1" should not be confusing or offensive to people who are currently betting; they wouldn't be required to give a limit price, anyway. The house would still, by setting the price after the bets are in, make sure its books are always balanced, and in fact all bets on a given horse would still ultimately go off at the same odds, so the reporting system wouldn't be different. People who placed bets that ended up ineffective would have to have their money refunded, which could be a logistical nuisance. If it would attract any significant number of new betters, though, it seems like it could make horse gambling more popular. Which no doubt would be reason enough for some other people to oppose it.
* I'd be inclined to call the system "unfair" except that pretty much anything that's upfront about its unfairness when you're going in seems to me ipso facto not really that unfair. There are probably exceptions to this rule (of what seems to me to be fair or unfair), but they're very uncommon.
† This makes it a lot like the Dow Jones Industrial Average.
‡ Kind of like a terms-of-trade effect.