In a set i find i prefer to continue until i think i wont get another full rep (i.e. not ‘failure’ as such, and yes - realistically there may be a rep or two left on many occasions)
Most programs call for set/rep schemes such as 3x8.
What would normally happen for me is something like 10,8,5 or similar if doing 3 sets with the same weight. I rest about a minute or less between sets, except on deadlifts (longer).
To get 3x8 i would have to lower the weight being lifted (either per set or overall) and/or lengthen the time between sets.
Other than to avoid heavy weights or get extra warm ups without realising it - what actually is the point of stopping at x reps just to stick to a set/rep scheme over a number of sets.
May work better with low reps, e.g. triples and fives.