Very little (if any?) safety-critical information is passed automatically between ATC systems and planes. The ATC controllers manually interpret their display screens, make decisions themselves, before giving out the equivalent of movement authorities (clearances) verbally. The pilots listen to the radio, and control the plane based on their understanding of the movement authorities received. The system->human->human->system is the basis for interoperability, but also the source of many miscommunications. By contrast, ETCS sends movement authorities directly from the signalling system to the on-board systems, without any of that information being relayed through a human.
There's also no interlocking in aviation movement authorities. For example, a controller can give permission to plane to land, while also giving permission to fire trucks to cross the runway at the same time. There's no engineering safeguards to prevent the controller from giving conflicting clearances. There's also no interlocking on the plane - if the pilots are given a restricted movement authority like "not above 200 knots" then there's nothing on the plane that prevents them from going too fast. ETCS has engineered safeguards to stop conflicting MAs being issued, and also to ensure trains stay within the MA they have received.
The equivalent would be if an ATC system calculated clearances, and those were sent as data over-the-air directly into the on-plane control system. That would mean each plane system would need to be compatible with every control tower system in every country, and every control tower system would need to be able to communicate with every different type of plane. That would be a huge coordination and system design effort.
You may be surprised how things have evolved over the past ten years.
CPDLC (CockPit Data Link Communications) offers direct communication between ATC systems and aircraft Flight Management Systems (FMS). ATC cannot send commands directly to the FMS but can send requests which the flight deck crew can choose to accept or reject. It does wonders for removing the scope for human miscommunication from the loop whilst still giving the pilot the final say.
There is some non-invasive functionality that does not have a human in the loop, such as requesting position reports.
There are indeed ATC systems out there that, based on crew requests for clearance, present the controller with the request complete with an assessment as to whether clearance is sufficient, giving the controller the ability to grant the clearance, either unchanged or with modification options.
This is only possible because of CPDLC standards of which there are 2: One primarily in use in North America and the North Atlantic (FANS), the other (ATN which is more an evolution of FANS than completely different) in Europe. Large blocks of airspace are closed to aircraft that are not logging on to CPDLC.
CPDLC is very useful in the cruise but does not work so well in densely packed terminal environments, mainly due to the time crews have to receive, digest and accept or reject instructions. It also doesn’t offer the situational awareness that traditional radio does - The ability to hear what other people are doing, which adds to the number of brains on the matter that could spot an error.
Conformance checking is another feature of many modern ATC systems: They can check data received from various sources and check that this complies with the data that a controller has recorded as having issued as a clearance to a flight: Route, level, QNH setting, etc. Computers are great at routinely checking such parameters, humans considerably less so! No system is infallible though.
With all of this potential capability I will be very interested to read the La Guardia collision report when it is finally available.
International aviation standards are however very slow moving beasts and it takes a long time from the concept of such systems to their sufficient adoption to offer meaningful benefit.