I'm going to attempt to give an answer to these two questions. I am going to do so without looking up any literature, so if I am wrong, please give a citation.
Re: hydride reductions
I think this can be complicated. A good leaving group can also result in a more electron deficient carbon nucleus. I would argue it is reactivity of the carbon that leads to the result rather than leaving group ability. (If all reactions formed a tetrahedral intermediate, then decomposition of it by the best leaving group would be fastest. I don't think they form or reversibly form a tetrahedral intermediate.)
I would argue that reduction of an acid chloride by HAl(OtBu)3[-] is an example of a very weak hydride donor reacting with a very reactive carbonyl compound. The product is less reactive and unable to react further.
The reduction of an ester can be done with a borohydride, but this reduction is also influenced by the Lewis acidity of the metal. Thus, LiBH4 is more effective in reducing ester than NaBH4 because lithium is a better Lewis acid (one of the forum moderators pointed this out to me). The method referred to by Disco appears to be a complexed borohydride reduction (from the abstract of the paper at least).
If I continue with the same reasoning, then reduction of a RCOOH with a hydride will first form a RCOO(-) anion and H2. A carboxylate will resist addition of a hydride compared to an ester, anhydride, or acid chloride. When reductions can succeed, they must also provide a method to convert what might have been written as a O(-,-) leaving group into something better, for example with a O=BR2(-) or O=AlR2(-).
Re: catalytic hydrogenolysis
I don't know the answer to this question, but I am a lumper. My preference is to assume that a given pair of electrons will behave similarly as we may know or may find in other reactions. I don't know the proof of the Heck reaction mechanism, but I felt you may find it logical. I therefore assumed a catalytic reduction might work analogously. Even if I am wrong, it may still provide a useful example to explain the chemistry found, for example the formation of trans olefins during catalytic reductions.
You can probably find tables that show which catalysts can be used with different substrates. This is data that could be used to hypothesis a mechanism or mechanisms for the reductions. What properties of the catalysts can be predicted from other reactions? I don't know the answer to the question, but I acknowledge the question is a good question. It is still a very complicated question with a lot of variables.