Food dispensers aren't a system that would require such idiotproof backups to idiotproof backups, tho. And there are limits to how much historical ballast you can carry on your ship before it sinks under the weight.
Indeed, saving of weight might be a good reason to go for modern rather than old solutions. Saving of space would be another. And both might take precedence over saving of energy, on a ship that by definition has shitloads of it available in all survivable circumstances.
It's a matter of speculation which old technologies would be ditched and which would be preserved. We don't and can't use 17th century food preservation methods on today's ships even though those might save lives when modern fridges break down. We opt not to have mechanical backups to electric flight controls on modern jets, realizing that the benfits of such backups would be mariginal at best, and that the .04% improvement in survival chances isn't worth the extra weight and bulk. Yet we have piezoelectric phones and even plain old shouting tubes aboard many modern warships as backup when the standard electric intercoms break down.
Dumbwaiters on TOS ships are perfectly plausible, then - just like swords in Dune, or message scrolls in Foundation. They are an aberration, but futuristic universes are tolerant of aberrations, just like our reality is (or else we wouldn't be using perverse things such as water closets any more). But they are also a symptom of a problem: of sticking to an interpretation that was made before the Trek universe around it had taken its full current form. TOS technology looks dated on the surface, which is a good reason to choose and interpret as much of the subsurface things as futuristically as possible. That way, we're still left with plenty of delightful anachronisms such as tinny-voiced computers, unworkably clumsy spacesuits, lack of visual contact with landing parties etc, but we have at least made an attempt to balance the equation. And we can keep on balancing it if it e.g. turns out that in our universe's 2020, devices that look almost exactly like TOS food slots are in general use and are based on photolithographic techniques or hyperaccelerated growth of foodstuffs. We just substitute the futuristic technology there, and then declare that the TNG replicators are more advanced still by a wide measure - even if this is not evident from the episodes, and as long as it is not contradicted by them.