I have a wooden threshold on an exterior that has some rot in it. Not
a whole lot, but some. Someone told me that it would be difficult to
replace, but probably much easier to simply dig out the bad part and
them pour in some mortar to fill it in most of the way, then top it
off with wood filler and prime and paint. That's easy enough, but I
was wondering why I would even want to do that when I could dig out
the whole thing, and replace it with some sort of cement product
that's designed to work good if it's only as thick as the previous
door threshold was. Isn't cement going to work better? As to some
background, the house was built in 1950 (Baltimore rowhome), and it's
a below ground basement door entrance where the offending threshold
is. This threshold acts as a lip to prevent water that does not go
down my drain hole from going into my basement, so presumably cement
would work better if I ever have a water problem in my back yard
(which I did have when I bought the house, but I've fixed that).

So, my question is to why I would even want to use a wood
replacement???
Everything else around it is also masonry (either bricks or concrete).