I'm pretty sure public executions aren't a thing for a reason... but with that being said, maybe just maybe it would deter people from committing other crimes?That would be better TV than anything that the BBC and C4 can come up and would be the highlight of the week if they actually showed it without blurring it all out at the moment we would like to see.
On the flip side of this argument, imagine showing a public execution and then 6 months later realizing they sentenced the wrong person? The fallout for that would be so massive and immense, it may actually scare the police and legal system to do a better job too!