I am estimating task time-to-completion using a sample size of ~36k. ~34k points are complete, ~2k are not. The response variable for my sample is right-skewed. I want to use this data to predict how long it might take a task to be completed. However, my end-user does not care about the exact number of days, they want something classified as "easy", "medium", or "hard", where difficulty is related to time-to-completion in some way. I am considering splitting up my completed data into those categories based on quantiles (exactly by thirds using time-to-completion), binning all the incompletes into the "hard" category (because at this point they've been outstanding for so long that if they were to be completed they would all be hard), and turning this into an ordinal regression problem. Is this dumb? If it is dumb, is there a way to handle incompletes outside of survival analysis? I'm wary of using it because I read it's not great for prediction.
Survival analysis isn't likely to be any worse for prediction than your proposed ordinal-outcome regression.
In the clinical survival context, the frequently used semi-parametric Cox model can get that reputation because it uses an empirical baseline hazard/survival curve, which might not generalize well to other situations (particularly with many clinical survival data sets containing only a few hundred cases from one or a few institutions). With a data set of your size, you might be able to get a good and generalizable fully parametric model, if you make an appropriate choice of baseline hazard function (Weibull, log-normal, etc.). At the worst, a Cox model should readily distinguish groups of relative task difficulties based on their relative "hazards" of task completion.
For your application, survival analysis has the advantage that you don't have to pre-define times to completion that represent "easy," "medium," or "hard"; the analysis itself should demonstrate that distinction.Your pre-chosen quantiles might not be the most useful breakdown of task difficulty.
As kjetil b halvorsen notes, you could consider setting this up as an ordinal-outcome regression problem, but he also recommends grouping by difficulty after, not before, the analysis. I don't see any particular advantage of that approach over survival analysis.