I think people kind of oversell the idea of Robin being around keeps Batman from flying off the handle. It was more how the two balanced each other out and how Robin was the light to Batman's dark and how Batman helped the Robin's develop as people from their personal tragedies and prior lives. In general Batman's surrogate family has a healing effect on him and the loss he continually deals with.
I just don't see it so much of a demotion from just an initial encounter, because continuity-wise we know that the more Supervillains popped up in Gotham the harder it became for Batman to do his job before Robin showed up and then Batgirl. I don't even see writers thinking they need to elevate Batman over Robin because Robin is already Batman's sidekick.Much like the firing of Dick post-COIE and later crawling back to the Bat-offices when the Titans brand fell off, it comes off as a demotion that elevates Batman even further over Robin by giving him even that much more experience.
The argument that establishing the character dynamics between Batman and the villain doesn't entirely work, because it's not as if it has to be mutually exclusive. With the simple writing of the older comics, it's not like it would have happened even if Robin hadn't been there. And in stuff like BTAS, Poison Ivy's first encounter was pretty much a villain of the week, and her more character driven episode "House and Garden" had Robin in it.
It may not be mutually exclusive but it was how a lot of those initial encounters in Post-Crisis were structured story-wise. I for one prefer where Robin comes in after Harvey Dent becomes Two-Face so we have that battle of the "partners" rivalry.
Ivy's first appearance entirely set up her character and motivations, though. Robin worked in "House and Garden" but did he need to be in her debut episode just because he was in the comics?
Isn't it always Bruce's choice, though? I mean, maybe there was one or two instances of Alfred suggesting the idea, but any neglect I can think of came less from Bruce putting the brunt of the work on Alfred and more Bruce being busy as Batman (particularly trying to find Tony Zucco or some major crime).