This is a very bad idea. Don't let your artists produce or export to the final format. Ever.
The typical workflow for artists is to use photoshop images (psd files) for their work and export textures as one of the compressed formats supported by cards, such as DXT1 or DXT5 or whatever.
It will all start innocent, the artists commit the DXT compressed textures and you are happy. Then you realize, that all textures are compressed as DXT5 instead of DXT1, even those without an alpha channel, because DXT5 has twice the bitrate and thus MUST HAVE twice the quality. You ask them to remedy the mistake but going through all the textures in the repo and reexporting them manually is too much work and apparently too error prone.
At this point, you can forget any efforts to get an automatic export running, because the DXT compressed versions, and the (presumably) source material somehow got out of sync. And there are multiple copies of the source material and noone really knows which ones are to most recent ones.
And then you consider to change the way the textures are compressed, or even the compression format, but your only viable source material are the already lossy DXT1/5 compressed textures.
It depends on your workflow and the discipline that is kept in the office.
Everywhere I've been the art budget was fixed in stone in advance. The maximum size of each model, both meshes and textures, is specified and is included in the acceptance criteria. If a single asset is over budget it is well known because it shows up on the feature dashboard that shows all the metrics of all the assets; it needs to be approved by the art lead, the art director, the feature designer, the tech lead, and the project manager. When it happens it is usually just "this is an important model" followed by "yup", "yup", "yup", "go ahead".
Since the asset sizes show up in several metrics and are reviewed daily, it would be fairly hard for an artist to slip in a 4MB dxt file without at least one person noticing.
If your art process is such that nothing gets reviewed and there is not accountability, sure, I'll agree it is a bad thing. But that is bad because of a (lack of) policy and a lack of discipline.