It is two decades old. I'm not really sure why that would be a problem; likewise, Unix is over 40 years old, even though it's quite possible that not a single line of the original code remains. A long pedigree can be and often is seen as a good thing. In the case of Bethesda's engine, unfortunately it's 14 years' worth of accumulated bugs and kludges rather than 14 years of refinements, which I think is the problem, especially with its perception.
Yup. So some refactoring and general cleanup might actually be enough to bring the current engine up to scratch and reduce bugs, without having to start from scratch. Even that could end up devouring man-hours, but probably would work out as less costly than replacing it outright and having to write most of that code anyway (with the additional problems of programmers having to familiarise themselves with it, and having to be careful about breaching IP's, assuming someone else owns at least portions of the current one).
At the end of the day, to figure out the best option one would have to both be an experienced engine programmer, have access to the actual code, and be familiar with the options available. It'd be great to here from some gamesas guys, but I expect they'd be reluctant to chip in (if not outright not allowed).