Can thrust reversers be set to automatically activate on touchdown?
Can it be done? Yes. Is it done? No. The consequences of unintended operations are serious.
To the best of my knowledge, no aircraft has the option set automatic thrust reverser. Using the levers are the only way to operate them. In fact, most of the design efforts have gone the other way- to ensure that thrust reversers are not deployed inadvertently.


In most aircraft, the Reverse Thrust Levers can be raised only when the Forward Thrust Levers are in the idle position. The thrust reversers have separate levers in front of the engine controls, which are prevented mechanically from operating otherwise.




Source: bloginblack.de


There are sensors installed in the engines which auto-stow the thrust reversers in flight.
The design philosophy of thrust reversers is that it is better to not deploy them when needed rather than deploy them when not needed i.e. they are designed to fail.


The main reason for such a design philosophy is safety. Any uncommanded deployment of thrust reversers in any phase of flight can have serious consequences.


Takeoff- If the trust reversers are deployed in one engine before $V_{1}$, the aircraft will veer off the runway. If it is deployed after $V_{1}$ and before $V_{2}$,the aircraft cannot achieve $V_{r}$ required to initiate rotation.
Flight- Deployment of thrust reversers during flight can lead to controllability issues.
Landing- Deployment of thrust reversers during landing practically eliminates the option of rejected landing.


Because of these reasons and reliability issues with thrust reversers, there is no option for automatic deployment of thrust reversers.