Of course. With higher rates, more would stay than do currently. Not everyone at the regionals is a 25 year old with no responsibilities, for whom moving to the majors offers a very clear betterment of their career/life. Even at the current rates, there are plenty of pilots who have determined that it's better for them and their families if they stay at their regional job. The higher the pay rates, the more of those pilots there are.

Further, the higher the pay rates, the more it makes sense for people to come to the regionals in the first place. Right now there are corporate gigs offering 1500 hr FOs more pay than some regional captains make. The LCCs and cargo are going to be hiring pilots at ATP mins with no jet time. If the regionals don't raise pay and quality of life, the regionals will have nothing to offer pilots other than a flow and quick upgrade. And in this hiring environment, the flow and a quick upgrade is worth far less than it used to be.

So yes, regional staffing issues are of their own doing. It's very simple. If they offered competitive compensation, benefits, and quality of life, they would have more pilots.