I train (CrossFit) and run in the minimalist Onitsuka Tiger Tai Chi (by Asics). To protect against the pounding of pavement, jumping rope, box jumps, etc. I create a full-length insole from PPT foam padding (orthotic grade material).
This has worked perfectly for me for a year now so I am currently experimenting with a similar set-up for tennis. Instead of the slipper-like Tai Chi, I'm using the very lightly-padded Asics Mexico with the same PPT protective insole. They worked very well at the my last tennis lesson: I was working on the backhand and my coach said my weight-transfer was not right. The minimalist shoes gave me superior feel to make the necessary adjustments. In this limited experiment of hitting with my coach I experienced no stability issues whatsoever. With "zero drop" there's nowhere to fall! I totally agree that the only reason modern tennis shoes requires lateral stabilization is because they have such an extreme heel drop.
I'm going to try the Asics Mexicos in a doubles match this evening, and will report back.
If the set up is suitable for match play, but I find that the Mexicos wear too quickly I plan to try the Merrell Barefoot Road Gloves.
I hope others will share their experience with minimalist and zero drop shoes on the tennis court.
Head Youtek Prestige Pro • Babolat VS Natural ThermoGut 16 Touch String Black • Merrell Barefoot Run Road Glove shoes