My guess is that while barristers might say, as in the survey, that they'd like the process of taking mid-trial instructions to be smoother, they would probably not appreciate having the client continually talking at them. That's partly for the practical reason that advocacy is hard enough without this, and partly because of expectations regarding the profession and how barristers/advocates operate.
Is there any law that would prevent defendants and defence counsel from turning up to court equipped with such headsets?
This goes under the general power of a court to govern its own operations. Even without specific legislation on electronic devices, a judge has inherent power to deal with conduct in the court that is affecting the administration of justice. A classic low-level example is someone eating in court - there's not a specific rule against eating, but judges will certainly tell the person to stop. It might be that they were eating so discreetly that there was no real disruption, but it's within the discretion of the judge to control the situation, and (if the instruction is not followed) to escalate the matter. That may be a contempt of court process if things really escalate but people, especially counsel, are quite likely to heed the earlier warnings.
In the same way, a judge could tell a barrister to take off his headset if the judge felt that its use might compromise the fair conduct of proceedings - for example, by the barrister being too distracted to present the case properly. The judge need not wait for that situation to materialize before intervening. It is safer to disallow the novel thing than to enter into a detailed investigation about it.
There are other related reasons why a judge would be liable to be sceptical about the headset idea. These would also be felt by the advocate.
Counsel has obligations to the court as well as to the client. Sometimes, counsel has to present and discuss weaknesses in their own argument. This duty may be compromised if counsel put themselves in a situation where the client is able to secretly complain about what they are saying in the moment.
Generally, counsel are meant to be independent from the client anyway in how they argue the case. This is an ethical obligation from the relevant regulatory bodies (the Bar Standards Board, the Faculty of Advocates, etc.) as well as something that's foundational to the legal understanding of how a barrister operates. In R v Farooqi [2013] EWCA Crim 1649, a defendant claimed to have had an unfair trial partly because of his barrister's overly provocative and offensive strategy, which was claimed to go beyond the scope of his instructions. On appeal, the Lord Chief Justice, Lord Judge, said (paras 107-108) that "the client does not conduct the case: that is the responsibility of the trial advocate [...] The advocate is not the client's
mouthpiece, obliged to conduct the case in accordance with whatever the client, or when the advocate is a barrister, the solicitor 'instructs' him," and that aside from a few special instances like how to plead, "the
advocate, and the advocate alone remains responsible for the forensic decisions and strategy". In a similar appeal, R v Ekaireb [2015] EWCA Crim 1936, the next Lord Chief Justice, Lord Thomas, opined that there is "no basis upon which an advocate can be instructed as to what to say in his closing speech by his solicitor or by his client or when to conclude it" (para 46). Therefore, there is no reason why a client ought to be able to give continual direction in counsel's ear, and a principled reason against it.
It can be asking for trouble if a client is having direct contact with the advocate, without their solicitor also being in the loop. Misunderstandings and confusion can arise. Where there is a solicitor, it's primarily the solicitor's job to instruct the advocate on behalf of the client. It is part of the Guide to the Professional Conduct for Advocates in Scotland to avoid situations causing that sort of conflict (4.2, 4.5 and 4.6). But I suppose we might imagine the solicitor also wearing a headset.
It may be hard to be sure about whether conversations are being recorded, or broadcast outside the courtroom. The fairness of the trial could be compromised if the defendant's privileged conversations are accidentally made available to others, which is foreseeable when it's a conversation over radio equipment rather than whispering in the same room. We can imagine that the walkie-talkies use some sort of encryption, but we also have to imagine that everyone involved is convinced that it all works properly. The judge would like to deal with the burglary, or whatever the case is, and then move on to other things, rather than take a side track down the road of whether the headsets are adequately set up.
There is a specific regime for live-streaming proceedings, including offences for making an unauthorised transmission of that signal (e.g.
the Courts Act 2003, part
7ZA for a
video feed to members of the public, but there are several other
legislative provisions of this type). Given that Parliament has
legislated quite carefully on the topic of how to handle (even
unintentional) video or audio transmission outside the courtroom, a
judge could reasonably be wary about opening the can of worms that
comes with permitting a novel use of radio equipment in court,
outside of any statutory framework to deal with the resulting issues.
There are some special instances to do with children or other vulnerable witnesses where a defendant can be disallowed from conducting their own defence, so that in particular they cannot personally question the witness. See for example the Vulnerable Witnesses (Scotland) Act 2004, section 6. The purpose of that provision would be defeated if the defendant could have their advocate parrot their words, or even if the child thought that was what was going on.
Finally, because of all of the above, introducing this novel element into the courtroom risks increasing the cost and complexity of proceedings. In addition to the actual criminal case, the advocate now has to argue about the technology and so forth. This is generally the opposite of what everybody wants, and cuts against counsel's duty to deal with the case "efficiently and expeditiously" (E&W Criminal Procedure Rules, 1.2(f)). The criminal defence bar is not high-paying, except at the very top end: for most advocates, the incentives are against taking the risk.