What are the advantages, disadvantages and current state of affairs for text-based ATC?
I'm a newbie pilot, but I wanted to give the obvious example that crossed my mind when I read your question. In the UK GA world we have to, for example, call up to say we're on final approach. Finals can be a pretty busy time for the pilot, and at any kind of busy GA airport you're likely to have something along the lines of the following discussion:
(Note in my example, my airport has an &quot;Information Service&quot; rather than full blown ATC, but nonetheless - the example stands)

Me: &quot;G-AB Finals, Runway 16&quot;
Tower: &quot;G-AB, Runway Occupied&quot;
Me: &quot;Continuing, G-AB&quot;

This is me telling the controller that I'm aware I can't actually land, but I'll continue flying my approach path down towards some kind of decision height - somewhere around 300'. If I hear nothing again, I'll go around.

Tower: &quot;G-AB, Land At Your Discretion&quot;
Me: &quot;Landing, G-AB&quot;

I now continue my landing, except I'm not happy with my approach so I now declare a go around

Me: &quot;G-AB, Going Around&quot;
Tower: &quot;G-AB, Roger&quot;

Remember that all of the above is going on while I'm setting flaps, keeping on the glideslope, watching the runway and maintaining my airspeed.
Now also, imagine the alternative:

Tower: &quot;G-AB, Land At Your Discretion&quot;
Me: &quot;Landing, G-AB&quot;

So I now have clearance to land. I carry on, there's a bit of a crosswind and I'm working hard. I cross the airport boundary and I'm concentrating on the runway.. Unbeknown to me, a small dog/child/whatever has broken loose and is charging across the grass to the runway:

Tower: &quot;G-AB, Go Around, I say again, Go Around&quot;
Me: &quot;Going Around, G-AB&quot;

In less than 2 seconds the danger is gone, and the tower know now that I've understood and acknowledged. Now in no world am I ever going to be looking down at a screen during that moment - even if a message came through and beeped/bonged or whatever - my concentration will be on landing. Now you might argue for a specific &quot;Go Around&quot; call/button or whatever - but how many of those different things will we end up with. I simply can't imagine a situation where I won't need my headset on and radio tuned.
I'm not saying any of this stuff will never come in, but pressing a button to talk and listen is much more favourable to typing or reading something during critical phases of flight. At best, I can imagine it complementing some of the more mundane messages and perhaps Ground Controllers.
An ATIS text system might be nice, and I imagine routing and similar will be useful - but I can't imagine it taking over voice completely. Sometimes you just can't beat talking - there's a reason people still e-mail the line &quot;I'll call you&quot;.
Beyond that - during those radio comms every aircraft in the vicinity now knows that G-AB is on Finals. This is incredibly important to GA traffic operating in VFR because pilots work hard to keep a mental picture of whose where - not to the degree the tower does, but if someone is following me but doesn't have visual (Very common - planes are surprisingly hard to spot), or loses visual, they know exactly where I am and what I'm doing.
The aircraft that's just touched the threshold also knows that control are aware the runway is occupied and hasn't just cleared an aircraft to land.