Recommendations are for free, so people are always happy to recommend doing more work when they are not the ones who have to do it. That being said, plotting data, including your predictions, is a good practice that will help you notice problems with the data that you have no way to know based on numbers alone (see the famous Anscombe's quartet, for example). Typing
plot(predicted, observed) or
plot(observed-predicted, observed) is really not that much work.
Of course, if you have 100 000 models, one for each gene, or each voxel in a brain, then nobody is checking residuals. (but maybe they should)
Edit, answer to comment: Many of the assumptions are important for inference but not for predictions, so if assumptions are violated but predictions are good, then it's not really a big deal in a sense that it won't make predictions invalid.
However, if residuals are not independent, that means that there is an effect in the data that you can model better, hence improving your predictions. If they are not normal, then you might consider using a more robust model., which would again improve your predictions (according to some metrics). Finally, if they are not homoskedastic, then you can sometimes improve model fit by modeling variance, or you can realize that you are using the wrong model e.g., Gaussian, instead of Poisson/logistic, and you can fix it and again improve your predictions.
I am not saying it will always make a large difference or that you must satisfy your assumptions, but sometimes it helps.