[villagetinker]

OK, this situation seems to be very different from what I am familiar with back up North, thank you to all that pointed out I may be wrong with my initial answer. So, to the OP, you can approach the 'owner' of the land and see what would be involved with implementing your idea.
I see the following possible problems:
1. The people living next to the right of way will not like golf carts close to their back yards.
2. The Utility company will want some form of indemnity for any accidents.
3. The Utility company will also need 24/7/365 access to this land for maintenance of the land (mowing, weed control, tree trimming, etc.) and line maintenance.
4. These areas are typically fenced off, so there will need to be some discussion about how to allow golf cart (and others like the typical multi modal path) access.
5. There are probably different arrangements over the years for different locations, I have seen golf courses under the lines, I have seen the previously mentions golf cart paths parallel the lines, but these uses were probably not in the older sections of TV.
6. There will be some expense to the utility for allowing these uses, so the associated CDD's will need to be involved.
7. The counties will need to be involved for the various road crossings, gates, lights, etc.
IMHO, I do not see this happening in the near future, but I do agree it is an interesting idea.