Of course it's possible. Whether or not it is desirable is a different story. Here are a few reasons it wouldn't catch on.
1. Basses with pre-installed wireless transmitters will only work with particular wireless receivers. This is kind of lame, from a production and marketing standpoint, because the basses will only be functional if you buy a particular piece of equipment to go with them. And furthermore, that equipment may eventually be outdated or upgraded. (Unless the basses are equipped with traditional output jacks, but reliance on them would defeat the point of having the wireless.)
2. Manufacturers would surely have to deal with certain compliance standards related to the use of wireless transmitters, and this adds to the cost and hassle of manufacturing and selling an instrument.
3. Bassists and guitarists have proven, time and again, to be very resistant to change, in regards to instrument technology. I'm sure many would view this as a novelty, and never take it seriously, even if it was indeed worth taking seriously.
4. It would be very easy to forget to turn the bass off when you're done with it. This is important, because wireless transmitters draw a fair bit of current, so batteries deplete very quickly. This is a user-error, of course, but even if it is silly, I have seen countless players express a preference to avoid active components on basses, because they are too worried about battery changes, and forgetting to unplug.
5. Similar to 4, the increased frequency of battery changes will probably deter people, even if they would have been fine with changing batteries in traditional wireless transmitters.
6. Similar to 3, complications to onboard circuitry tend to cause some people to fear the increased likelihood that something may fail, and leave them without a bass to play for a gig, or whatever. Though the inclusion of a traditional output jack as a failsafe, should alleviate this fear for most people.