Why it seems that there is no counterpart function as to multiplication, to `Total` as to addition?

In addition to the previous answer...

I designed and implemented Total 17 years ago. Its first version was named ListSum. The primary reason for ListSum's implementation was to encapsulate the functionalities dealing with error accumulation while summing a list of numbers. (A well known phenomena in, say, numerical solvers for ODE's.)

Of course, I also considered ListProduct, having analogous functionality. But there was not really a strong reason or use case for it.

(During the final design phase Stephen Wolfram renamed ListSum to Total.)

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@tomd

My memory of things is that before Total, Tr@lst was considered faster than Plus@@lst if lst was a packed array, an observation Ted Ersek attributes to Rob Knapp

Rob Knapp was supervising my work on the Total project.

Total is different from Plus@@ because it uses tricks to minimize round-off error. It is thus a useful addition to the toolkit. Times@@ doesn't suffer from the problem, so no similar function is needed.