yes Childwall Blues, I agree with your sentiments too. The area of Beechwood is a considerable size in Runcorn and being close to the Halton - Frodsham line, I think a station could be built on that line to serve that community especially with trains direct to Liverpool. By doing this, it would leave Runcorn Station to serve its main core of business which are the I/C trains to London and Birmingham.I do not think many would share your opinion.
However, this possibility could only happen if trains to / from North Wales (not solely Chester) go to / from Liverpool Lime St. To me that is the real reason for reopening the line to everyday passenger trains not just a "local" service between Chester and Lime St - that to me seems pointless and a waste of time given there are reasonable alternatives.