My thoughts on DoT:
There isn't a problem with DoT if it is done correctly. For example Swain and Malzahar have pretty good examples of DoT done right because their DoT encourages interaction between them and their opponents. Swain's DoT amplifies his damage and encourages him to brawl. A Swain that simply throws his E out and walks away isn't going to be that threatening. He gets the most out of his DoT when he combos it with Q and autos which provides the enemy laner an opportunity to retaliate.
Similarly, Malzahar's DoT, while very high damage (320 + .8 AP total), is very short range (650) has a rather high CD of 7 seconds, and is his main form of wave clear while in lane. This opens up many different opportunities/choices for him and his opponent to play around.
An example of an unhealthy DoT is Cassiopeia's old Q. It was on a short CD - 3 seconds, did high damage (235 + .8 AP at max rank), decent range (850), and provided Cassio with a big MS boost to weave in and out of retaliation range. The problem with this is that it is largely non-interactive. The range, MS boost, low mana cost, and spammability combined to make a very frustrating to lane against enemy because if she was hitting her Qs, she could wear her foe down while having enough mobility to completely avoid interacting with them if they tried to go aggro. The result was that you often couldn't beat her in lane unless you had some jungler interaction or you were playing somebody who could engage on her from out of her range like Lux, Xerath, or Syndra.
DoT readability also comes into play here. When a player gets hit by a Syndra Q, a spell very similar to Cass Q, the damage is instant, and from a readability and decision making perspective, that player will be able to tell if they are in immediate danger or if they can afford to all-in. With DoT, the readability and decision making becomes somewhat clouded, especially in team fights when it is hard to tell where exactly damage is coming from and the ticks from DoT get lost in the chaos. I believe this is something that can be overcome with some clever visual cues.