The Red Scare was not about catching actual spies. The USA already had law enforcement agencies for that task. Instead, it was about finding and publicly outing potential spies. People who might be sympathetic to the Russians (or vulnerable to blackmail by them), and thus might in the future commit an act of espionage, if given the chance. For instance, during this era this logic was used to fire an astounding amount of people from government jobs for homosexuality (at its height, it was about 2 a day).
By and large the people pushing the scare were looking for publicity for themselves. An actual spy doesn't help that cause all that much, because the bulk of the publicity surrounding their case will go to government enforcement agents and lawyers.
If you aren't one of those, by far your best target would be someone who can't actually be proven to have committed a crime, so you can just keep bashing them yourself as long as the media will listen to you. Even better if its someone famous, or someone that some people will want to go to the news to defend. That will help feed the story.
I don't believe there is a good way to measure how many (or if any) incidents of actual real-life espionage this might have prevented. Its possible that fear of the witchhunt itself made government officials vulnerable to foreign agents, so it may have even been negative. There's really no way to tell.