I like the way you think. It makes perfect sense on the surface. But the music industry and legalities surrounding it are complex. There are a few reasons why this practice has not become common in the music industry.
First, many artists for one reason or another, do not wish to allow their music to be licensed or reproduced in a karaoke version. I can't think of a compelling business reason for this practice, but there is a long list of famous artists who are on the "karaoke no-fly list" who won't authorize any legal reproduction of their music for karaoke. Perhaps it's an ego thing where they don't want some inebriated American Idol wannabe butchering one of their songs at a karaoke bar.
But the main reason record labels and music producers don't produce their own karaoke or instrumental versions of the songs they hold the rights to, is that it is more profitable for them not to! Let me explain.
When a popular song is released, there becomes a demand for instrumental and/or karaoke versions of the song. Other folks want to sing the song, so they are willing to pay for an instrumental or karaoke version. There are several companies who have created a business of "reproducing" popular songs as instrumental or karaoke versions so they can sell copies of those reproductions and make a profit.
In order to legally reproduce a song, a company or individual must negotiate with the owner of the rights to that song for reproduction rights and distribution rights. Up front fees as well as royalties as a percentage of all sales are usually a part of the deal. The rights holder (such as a record label) can sell the reproduction and distribution rights to several different entities who will do the work for them of marketing the reproductions to the target market who wants to buy instrumental only or karaoke versions. The holder of the rights to writers royalties, will usually be entitled to a small percentage from each sale as part of the overall deal as well.
If the record label produced an official instrumental only version themselves, the companies who are in the business of replicating and reproducing the songs would not want to buy the rights to reproduce and distribute a song if the original recording (sans vocals) was available for the public to buy. After all, how can you reproduce a version more authentic than the original? So the label would miss out on multiple opportunities to make deals with multiple companies to sell the right to reproduce the song and distribute those reproductions.
Also, the companies who buy the rights to reproduce and distribute the songs, will spend their own money marketing and selling those reproductions, and the record label and whoever holds the rights to the writers royalties, will get a percentage of every sale. So someone else is spending the marketing dollars to increase the revenue from the song.
It would be interesting to see what could happen if a record label released an official instrumental version. They might discover that they could sell many copies. But for now apparently, they feel there is more money to be made selling the reproduction and distribution rights to the companies that specialize in the instrumental only and karaoke markets.
I don't really have an answer for why it does not seem to be possible to buy the original producers project files. It may have to do with a legal question of some implicit right to reproduce the music from those project files without paying for the reproduction and distribution rights. In other words, if I pay you for your project files, does that give me the right to use those files to produce a derivative work without further payment to you since I already paid for the project files? There might be a way an implied right of use could be construed that might preclude further obligation for payment of reproduction/distribution rights.
Also, sale of the project files may not give the songwriter or composer any mechanism wherein they could be paid any writers royalties on derivative works produced through the use of those producer project files. Perhaps it's like opening an untested "can of worms" or "pandora's box" to use a few cliche's.
There may be other reasons as well, but the foregoing provides one explanation.