Some anglers are concerned that the wood might interrupt the rod's action. That is, the added strips might stiffen the butt section too much. Well, harder woods like ebony, oak, maple, & others will stiffen the butt section more than soft woods. Those woods are also more difficult to work with than the softer woods. All that being said, the wood should not have a damaging effect on the rod's action - assuming that the rod is properly designed.
I find woods with some flex to them are the best for most rods. Cedar was traditionally the most often wood used, though I suspect that was due more to it's availability & color contrast with the bamboo rather than how it functioned in the rod.
I really like using poplar wood or bamboo strips that have been flamed either darker or lighter than the bamboo used in the rod. The poplar is soft & flexible in addition to really giving the rod's appearance some "pop". Poplar tends to get a bad reputation in wood working, being used as the secondary wood in drawers & other furniture parts. But some craftsmen recognized it's beauty & used it as a prominent wood in details on very expensive pieces of furniture. The bamboo's color can be manipulated to contrast with the cane in the rod & it will flex at the same rate as the rod. Both are easy to work with, too.
Just about any bamboo rod can be mortised, but keep in mind that a short rod with a stiff (or hard) wood will make for a stiffer rod. Longer rods are less effected by the extra wood in the grip & reel seat areas. In my experience, the best mortised rods are those that avoid extremes in design. Other than that, the sky's the limit on what is possible which is why these rods are some of the most attractive fly rods you'll find.