There are several problems that we face. We deal with this all the time developing new products.
1. Many of the products out there were designed a long time ago when standard batteries were all that were available, and we are now stuck with them.
2. Low-cost rechargeable batteries have a lot less power than a standard Alkaline type.
3. The user must be able to EASILY get a battery in an emergency. The guideline was whether or not you can get it at Radio Shack.
4. Rechargeable battery technology is changing very fast. You can hardly get Ni-Cads any longer, and the latest consumer technology is Lithium Polymer, with Lithium Titanate on the Horizon. All use different charging technology and they are not interchangeable. If you design one in, it may no longer be available in 5 years, while you are still using your equipment.
5. If an item uses a standard type cell, it is usually not possible to use a rechargeable. The reason is that someone will put in a standard cell and try to recharge it - this is very dangerous, so many manufacturers avoid this.
6. Sometimes you don't have the space for a standard cell, so you have to get a custom battery pack made.
THE REAL QUESTION is WHY aren't our equipment manufacturers putting phantom power capability into our amplifiers so we don't need batteries? This has been used for 40 years in the studio, sending DC power up the audio cable to power microphones. It is NO PROBLEM to send 6-12 V up the standard guitar cable to power our effects and guitars. Our engineers have solved the technical issues years ago. It makes no sense that the manufacturers are not interested.
Perhaps it is a "Chicken and Egg" issue - no one will do it unless there are products available to use it, etc. One of the big makers - Fender, Peavey etc. could do it as they supply both ends and get the ball rolling.
My 2 cents.