Firstly, it is worth noting that the blocked radio transmission is only one point on a very long list of factors that caused the horrible accident on Tenerife. There is enough redundancy in aviation systems and procedures that a single fault somewhere in the system will [almost] never be enough to cause an accident. Weather, stress, a terrorist attack, company policy, poor CRM and many other things were also contributing factors.
Communication between air traffic control (ATC) and pilots is mostly based on simplex radio. Simplex radio only allows one station per channel to transmit at the same time; if two stations transmit at the same time, the signal will be blocked. Sometimes, if one signal is stronger, it will be possible to hear that signal but not the other. The main problem is that the two stations transmitting will have no way of knowing that they are blocking eachother. This limitation regularily results in various incidents - for example, when there are two aircraft with similar sounding radio callsigns on an ATC channel, one crew might mistake an instruction for the other flight, thinking it is actually meant for them. If both flights read back the instruction at the same time, neither of them will hear the readback from the other aircraft and realise the mistake, and ATC might hear just one of the readbacks, and not realise that both flights are following the instruction meant for just one of them.
So why isn't there work being done to phase out simplex radio in aviation?
There is. It's called CPDLC, or Controller-Pilot Datalink Communications. (Other, similar systems exist as well, with different names. In the following I will just discuss CPDLC).
CPDLC is a digital system that allows ATC and pilots to communicate via text. It is already widely deployed in many areas, one example being Maastricht UAC, one of the busiest area control centres in Europe. Multiple stations can transmit at the same time, without the risk of blocking other transmissions.
So why do we still have simplex radio?
So far, CPDLC is only used for area control. In areas where ATC instructions are time critical, such as an approach or aerodrome environment, we still rely on simplex radio, because it is guarenteed to be instantaneous - and pilots are used to acting immediately to a voice instruction. However, it should only be a matter of change of procedures and appropriate training before CPDLC can be used in all phases of flight.
More importantly, aircraft equipment is expensive. Replacing a simplex radio with CPDLC equipment involves a significant cost per aircraft. While this may be feasible for large airlines, remember that they only make up a part of flights. There are thousands and thousands of private planes, balloons, gliders and whatnot, and private pilots or flying clubs may simply not have the funds to implement CPDLC. And obviously, ATC can't turn off their simplex radio until everyone has equipment to replace it.
Another disadvantage of CPDLC, or other communication equipment that allows direct communication between cockpit and controller working position, is that it reduces situational awareness. A big advantage with simplex radio is that everyone has to listen to what everyone else is saying, since you can't talk when someone else is talking. This gives pilots the possibility to establish a mental picture of the traffic around them, which ultimately increases safety. As we saw with Tenerife, the lack of such a mental picture can result in tragic outcomes. However, simplex radio has probably prevented many other accidents, because everyone on the frequency knew what was going on around them. The Providence incident of December 1999 comes to mind as one example among many.
So, is there a solution to radio interference? Yes, there is. Is it easy to implement? No, it is both technically and financially difficult. Will it necessarily prevent accidents such as the one on Tenerife? No; a thorough safety and risk analysis must be carried out before deploying it everywhere.