I very much agree with the conclusion to the OP, because I too think there is value in DoTs and DoT champions, yet Riot have had trouble implementing proper gameplay around that for quite some time. Up until now, DoTs have mainly just been treated as a different, less clear form of nuke, and that is also what has pushed Riot to compress some of them into more instant burst, as is the case for Ryze's new kit. This I think is kind of misguided, because I personally believe DoTs can have a lot of unique gameplay of their own, and could have much more clarity with just a few UI changes. I think even Riot talked about this when reworking the health bars, but there was mention of displaying DoTs and HoTs on the health bar as differently-colored portions of depleting or regenerating health. Doing so would finally allow DoTs to have their exact value displayed for everyone to see, and would give them a lot more clarity as a result.
In gameplay terms, I also think DoTs have intrinsic value relative to instant nukes in that they can offer opponents more options to fight back. Because DoTs happen over time, having more of them could establish a greater difference between champions with lots of static health, who are good against burst but not to persistent damage, and champions with a lot of sustain, who are weak to burst but who can heal through DPS. Additionally, particularly prolonged DoTs could create situations where they'd be guaranteed to kill a target, but would give their victim the time to retaliate: one missed opportunity with Talon's DoT, for example, is that it could have turned his victim into a dead man walking, guaranteeing their eventual death but giving them an extra window of time to fight back as he escapes. Similarly, it would complement Singed and Fizz's hit-and-run gameplay much more, and could allow more champions to inflict "burst" in a less bursty manner, thereby making them a little more interactive.