No problems using a directional - in fact a bit easier than with a TT.
I have been teaching new kitesurfers on directionals.
You can not jibe till later, but easy to just drop, turn the board around, and start the other way.
You will get many different views on straps or not.
But it is possible to use the board you will use later, for learning, as sizing is the same - no problems.
A more advanced board is not more difficult to ride.
The "real" problem will be, you dont know till after a long time, years most likely, WHICH waveboard you prefer.
But no reason to go for something "beginner" like - going for a low cost cheap one is a good idea, for learning.
If you ask me I would:
Start having straps, when you learn to kitesurf.
When you can ride reasonably back and fourth, take them off, so you learn how to handle and "feel" the board and edges and how weight distribution changes everything.
This way you will learn to master a directional, and now you are free to either continue without straps, or put straps on for more extreme and aggressive surfing and jumps if you like the latter.
Peter