Yes, but these only work for calculating indices within []; many times you might wish to calculate indices outside, such as in the OP. Hence, the motivation for EndyIndexes.jl, this suggestion for $begin and $end, and EndpointRanges.jl. (Not to mention, the motivation for the @view macro, @jishnub’s OrdinalIndexing.jl, and this thread.) The suggestion to do arithmetic with first and last is just to use existing singleton objects, instead of introducing new start_ and end_ or ibegin and iend objects.
Additionally, because first+x and last-y could return special from-start and from-end indexing objects, they could be used for efficiently indexing strings by character (instead of by byte). For example, I’d imagine "αβγ"[first+1:last-1] would return "β" (with getindex making appropriate calls to nextind and prevind under the hood).