Can someone explain to me why are we sending a Tesla to Mars? I mean other than shits and giggles, is there any value in having it there? I assume putting stuff in the space is expensive and I wonder if that effort couldn't have gone to something more useful like a robot to look for water or whatever.
This was a demonstration launch, so no paying customer. The alternatives are (1) sending a rock or (2) spending months and millions of dollars designing a spacecraft capable of doing something useful. Option 2 is out of the question, option 1 is boring :)
The short answer is: no. You're talking about an entirely different mission profile, at far greater difficulty and at a radically greater cost.
You need an advanced robot, reliable, highly tested, constructed by the best rover engineers on the planet. You need to spend years designing the overall program. You need to deliver the robot safely to the surface of Mars. You need to operate the program at non-trivial cost for an extended period of time to then look for water etc.
For it to go to the mars we would have to be at the correct transfer window (or have a much higher Delta-V margin, which maybe BFR would be able to manage, but not necessarily Falcon Heavy). So it is not going to Mars.
Then, there are other costs. Cost of launch could have been absorbed by Tesla. Cost of developing a mars-capable payload would be extra. Who would pay for it, on a completely new and experimental rocket?
First flight of this vehicle configuration so it's a test flight. Most other test flights would just use a concrete mass simulator. Elon thought of something more interesting.