This question has two parts:

###Protecting the US audience

1. To demonstrate the US government's strong confidence with the US intelligence reports about *an evil role* of the Russian propaganda and to show its commitment to put all the necessary efforts to prevent such actions in the future;
1. To convince the US citizens that the Russian propaganda advertises *anti-American ideas and concepts*, undermines the key concepts of the US democracy;
1. To make it impossible for Russian propaganda agencies *act as financial proxies*;

This article sums it up in three paragraphs — [Reuters](https://www.reuters.com/article/us-russia-usa-media-restrictions-rt/russias-rt-america-registers-as-foreign-agent-in-usa-editor-idUSKBN1DD25B?il=0) (highlight mine):

> *U.S. intelligence agencies said in a report in January that the television station, which broadcasts on cable in the United States, is “Russia’s state-run propaganda machine” and that it **contributed to the Kremlin’s campaign to interfere** with last year’s presidential election in favor of Republican Party candidate Donald Trump.*

> *After that report, the Department of Justice insisted that RT America comply with registration requirements under the Foreign Agent Registration Act (FARA). **Under the act, RT will be required to disclose financial information.***

> *“Americans have a right to know who is acting in the United States to influence the U.S. government or public on behalf of foreign principals,” said acting Assistant Attorney General Dana Boente.*

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###Losing influence on Russian audience

> this gives Russia an excellent excuse to force Voice of America and Radio Free Europe/Radio Liberty to register as a foreign agent

The alleged brainwashing of a US citizen by "Russia Today" and the alleged brainwashing of a Russian citizen by RFE/RL, VoA, CNN, and Fox News are simply two different things:

**An average US citizen** influences the US policy. By voting on *real* elections, enjoying free speech, and finally, being able to make pressure on their Senator and convince other US citizens.

Also, it can be unclear for them that there exist mass media created solely for propaganda purposes, in each and every program, including "weather reports" talking about [perfect weather conditions for airstrikes](https://www.theguardian.com/world/2015/oct/05/perfect-weather-for-airstrikes-russian-tv-forecast-sets-sights-on-syria). A naive person watches it and starts believing the lies (*"can't they, finally, push propaganda in each and every word? there's no smoke without fire, so they must be right at least partially!"*)

Hence, spoiling an US citizen with an evil propaganda may have big effect and even may cause chain reaction.

**An average Russian citizen**, on the contrary, **knows** for sure that the US and ["Gayrope"](https://www.urbandictionary.com/define.php?term=Gayrope) want to conquer Russia and take all its natural resources.

Also, they in no way participate in their government's policy.

Even, the very word "a Liberal" is almost a pejorative in modern Russian language.

So, telling an average Russian citizen that "Radio **Liberty**" is a bad, bad, bad enemy agent would arguably have low effect, if any.

---
Also, any accusation of unfair oppression would be countered with a simple argument: other countries' official media already register under FARA:

> *"Foreign government-owned news organizations, including **China Daily**, the English-language newspaper owned by China’s government, **register under FARA**. The law applies to companies that are owned or controlled by foreign governments.*" — (same source)

OTOH, [allegations of selective enforcement](https://en.wikipedia.org/wiki/Foreign_Agents_Registration_Act#Allegations_of_selective_enforcement) have also been reported.