Meh, the only effect will be that public will not be able to follow their trades because they will be trading indirectly using 3rd parties.
https://stallman.orgtel:+12022243121
US citizens: call on Congress to prohibit members of Congress from owning stocks. If you phone, please spread the word! Main Switchboard: +1-202-224-3121
Discussion
It doesn't matter if the right or the left want this. The effect will be the same, and it simply will not work.