Update 2 (interpreting "faster" in terms of efficiency because it seems easier to measure)
The question has been updated but I still don't see a reference for insects being more efficient than mammals. Therefore I investigated this and did not find convincing evidence that it is the case.
Granted, the means of measuring efficiency are not necessarily comparable, but nonetheless it appears that ruminant cellulose digestion efficiency is comparable to overall distribution of cellulose-digesting bacteria.
(Overall, in both clades, the vast majority of species do not appreciably digest cellulose, so I focus on those that do.)
This paper suggests that while termites have remarkable ("nearly 99%") efficiencies they are a dramatic outlier among insects. In different groupings efficiencies range from 12-68%, 40-90%, and 11-50%.
This paper suggests that the "digestibility" of cellulose by cattle is in the range 0.7-0.8 (that is, 70%-80%). It is observed that the rate is higher in sheep (and goats?), though comparable figures are not provided. Other figures in the paper are in terms of animal body weight gain, which is unfortunately a poor measure due to the high energy cost of just living for warm-blooded animals.
If I interpret these numbers correctly, this means that ruminants in fact compare favorably to most celullolytic insects in their cellulose digestion efficiency. The very high efficiency of termites specifically is likely a facet of their being little microbial factories with legs; they are definitely an outlier among insects.
In conclusion, I don't think that there is any particular intrinsic advantage for insects in cellulose digestion.
I went back and read the linked post and realized that much of my answer was covered there and thus somewhat duplicative.
What is not covered is the insect/animal comparison. I do not see the source material for the assertion that insects are more efficient at cellulose digestion, it might be true or be somewhat trivially true but I would need to see where you got this information to assess it.
I would suggest doing a little initial research to maybe get closer to an answer. For example, here is a review on cellulose digestion in insects, and here is a resource for mammals, here is a comparison between the two.
Neither insects nor mammals (as far as I know) have the appropriate digestive enzymes to digest cellulose efficiently on their own. However, some special animals like termites and ruminants have assemblages of microbes in their gut that can break down cellulose. These enzymes are called cellulases.
However using these assemblages efficiently requires an extremely specialized gut system such as the rumen.
So you might get humans to digest cellulose by making transgenic humans with cellulases in their digestive system or completely redesigning the human digestive system. Possibly there would be a way to supplement with cellulase the way some people do with lactase.
A different concern might be that human physiology isn't set up to support that style of nutrition. For example I imagine that diabetes incidence would increase. But it's hard to predict.
If the idea is to feed a growing population of earth in a less carbon-intensive way, there are likely less complicated ways to do that by altering diet to e.g. less meat, popularization of sea vegetables, etc. But that's just my opinion, maybe you had something else in mind.
Hope that helps.