At beginning of update, TUF client try to update root role,but most of time there is no update of root role. For a check for updates step, at lease 2 download is needed (n+1.root.json and timestamp.json if there is no update)
if record version of root role in snapshot role, we can fetch timestamp role first, and update it when timestamp role changed and snapshot say it need to update.
On security way, I think it is the same because if the attacker can return fake snapshot,he also can pretend that there is no n+1 version of root role