a lot of 1st downs and TDs are thrown short and run in. I have never really seen an OC run what you're suggesting to be honest, it's super common to throw short and try to get YAC for the conversion for a reason
also keep in mind that you would do well to pick up most of the yards on third and longs at midfield/field goal range because it allows you to get better field goal range or set up for fourth and short. In either of those scenarios you may be punting/taking a 50 yard FG by not getting 9-10 easy yards. There was one to Rex for 7ish yards and he was stopped 1-2 yards short of the first down, but this increased the odds of the kick going in quite a bit.