Is there any reason to not just switch to 1-based indexing if we could? Seems like 0-based indexing really exacerbates off-by-one errors without much benefit
That said, I'm not sure how 1-based indexing will solve off-by-1 errors. They naturally come from the fencepost problem, i.e. the fact that sometimes we use indexes to indicate elements and sometimes to indicate boundaries between them. Mixing between them in our reasoning ultimately results in off-by-1 issues.
With half-open intervals, the count of elements is the difference between the interval bounds, adjacent intervals share 1 bound and merging 2 adjacent intervals preserves the extreme bounds.
Any programming problem is simplified when 0-based indexing together with half-open intervals are always used, without exceptions.
The fact that most programmers have been taught when young to use 1-based ordinal numbers and closed intervals is a mental handicap, but normally it is easy to get rid of this, like also getting rid of the mental handicap of having learned to use decimal numbers, when there is no reason to ever use them instead of binary numbers.
My opinion is that 1-based indexing really exacerbates off-by-one errors, besides requiring a more complex implementation in compilers, which is more bug-prone (with 1-based addressing, the compilers must create and use, in a manner transparent for the programmer, pointers that do not point to the intended object but towards an invalid location before the object, which must never be accessed through the pointer; this is why using 1-based addressing was easier in languages without pointers, like the original FORTRAN, but it would have been more difficult in languages that allow pointers, like C, the difficulty being in avoiding to expose the internal representation of pointers to the programmer).
Off-by-one errors are caused by mixing conventions for expressing indices and ranges.
If you always use a consistent convention, e.g. 0-based indexing together with half-open intervals, where the count of elements equals the difference between the interval bounds, there are no chances for ever making off-by-one errors.
"Is there any reason to not just switch to 0-based indexing if we could? Seems like 1-based indexing really exacerbates off-by-one errors without much benefit"
The problem is that humans make off-by-one errors and not that we're using the wrong indexing system.
Programming languages are filled with tiny design choices that don’t completely prevent mistakes (that would be impossible) but do make them less likely.
There are better programming languages, where you do not need to do what you say.
Some languages, like Ada, have special array attributes for accessing the first and the last elements.
Other languages, like Icon, allow the use of both non-negative indices and of negative indices, where non-negative indices access the array from its first element towards its last element, while negative indices access the array from its last element towards its first element.
I consider that your solution, i.e. using array[length] instead of array[length-1], is much worse. While it scores a point for simplifying this particular expression, it loses points by making other expressions more complex.
There are a lot of better programming languages than the few that due to historical accidents happen to be popular today.
It is sad that the designers of most of the languages that attempt today to replace C and C++ have not done due diligence by studying the history of programming languages before designing a new programming language. Had they done that, they could have avoided repeating the same mistakes of the languages with which they want to compete.
You should prefer a language, like Rust, in which [T]::last is Option<&T> -- that is, we can ask for a reference to the last item, but there might not be one and so we're encouraged to do something about that.
IMNSHO The pit of success you're looking for is best dug with such features and not via fiddling with the index scheme.
We can't choose to switch to 1-based indexing - either we use 0-based everywhere, or a mixture of 0-based and 1-based. Given the prevalence of off-by-one errors, I think the most important thing is to be consistent.
To use the terminology from the article, with 0-based indexing, offset = index * node_size. If it was 1-based, you would have offset = (index - 1) * node_size + 1.
And it became a convention even for high level languages, because no matter what you prefer, inconsistency is even worse. An interesting case is Perl, which, in classic Perl fashion, lets you choose by setting the $[ variable. Most people, even Perl programmers consider it a terrible feature and 0-based indexing is used by default.
You'd just get a different set of off-by-one errors with 1-based indexing.
So yeah, no. People smarter than you have thought about this before.