Way back in a previous life I did alignments at a large chain store.

The company policy was that tubes do NOT go into tubeless tires. The claim was that it would build up heat beyond the level that the tire was designed for. Seemed reasonable to me.

On the other hand, it could also have been over-the-top CYA.

I would make the argument that aging, dry tires that don't seal well at the bead or somewhere else are already a concern that should keep their use and speed to minimums, even before any concerns about heat build-up from adding tubes.