The cost of implementing a system to issue all of the competitors identical pistols for each match disqualifies your idea from the get-go.
Bingo.
There's no shortage of people with no experience with administering a match who make posts on the internet along the lines of "Competition shooting as it is now sucks, and here's why..."
That said, I'm aware of a couple of matches that have undertaken what the OP is talking about.
The Allegheny Sniper Match awhile back used identically configured FN bolt action rifles with an option to buy the gun at the end of the match.
Locally, there was an action pistol match here several years ago that had all of the shooters using identical 1911s.
The problem with the OP's suggestion is one of logistics. In the case of the Allegheny match, the match organizers had to secure rifles, scopes, ammunition, slings, etc. from various manufacturers who were willing to provide them, pretty much at their cost.
For the pistol match, the entry fee for the match essentially included the purchase of a 1911, ammunition, holsters, and mag pouches.
Matches like this do exist, but the fundamental problem with them is that they are either prohibitively expensive for either the match director or the competitors. As something that you could run as a special match maybe once a year, that's fine, but there's no fundamental way you could run such a match on a monthly basis.
Even if you posit the notion of buying all of the equipment beforehand, issuing it at the match, and collecting it once the match is over, you're still going to have to deal with all sorts of logistical issues:
• Who provides the ammo every match?
• How is that ammunition paid for?
• How often are you going to replace the guns/holsters/magazines/mag pouches?
• Who ensures that the guns are all operating to the same functional level? After all, in order to keep things fair, you're going to have to add a gunsmith to the match staff just to ensure that everything is above-board.
• How do you keep people from cheating, e.g. "I know that gun number 6 shoots slightly more accurately than all of the others, so I'm going to make sure I get that one issued to me."
• Administratively, how do you deal with competitors who claim that they lost out due to receiving a gun that was out-of-spec?
In order to account for all of the above things, the match fees are going to have to be raised to cover the cost of gun maintenance, provide ammunition at every match for every competitor, and replace worn out magazines, holsters, and other gear.
As it stands, the average local match has an entry fee of between $15-$25. To do what you're suggesting would probably require a match entry fee of $50 or more, every month.
Most local matches have a hard enough time accumulating enough staff just to set up the stages and run the administrative side of things as it is. To pile a number of further requirements on top of that would probably result in a match that would be impossible to administer without adding to the number of staff members, would result in a much higher per-match fee for every competitor, and would probably be less fun, as it would require you to use a gun that may or may not be functional.
I compete in USPSA Production Division with a S&W M&P, and the only work that has been done to my gun is a trigger job. Other than that, the gun is bone stock. Such a trigger job is quite common among Production shooters, but to claim that it gives a game-winning advantage would be overstating things by several orders of magnitude. I've seen plenty of competitors using bone-stock guns who've placed at or near the top. Most of the modifications allowed under Production Division fall under "a thing that I personally prefer, but doesn't really offer a true competitive advantage."
After all, no matter how awesome my trigger job is, it's not going to make a difference if the guy I'm competing against finds a faster way to complete a stage. The practical shooting sports are much more about mindset than they are about equipment, even at the highest levels with shooters who are running $3K Open Guns.