They CAN see what accounts move specific questions, but no one is looking at that. Last year when we had an Oath YA Team for a few months, we were told they couldn't see who moved questions so unless a user confessed, they could take no action. However, back before Yahoo was sold to Verizon, abusive question movers frequently got busted down to Level 6 when users provided the YA Team with links to questions that were being abusively moved (so clearly, it's possible to see what accounts move the questions...but it may depend on the ability of the Team member doing the looking and where they have to look to see that activity).
With no YA Team anymore, there's no one to contact who will bother to look into the abuse (users have been trying to get action taken on this problem for years). Yes, the powers-that-be COULD find out who was moving questions abusively and they COULD suspend the account or bust it down to a lower level, but don't expect that to happen any time soon. YA doesn't appear to mean enough to Verizon Media to put forth the money and resources it would take to get the site cleaned up and working properly.