Nurses hold many different roles. Saying you're a nurse is like saying you're teacher. Is that a pre-school teacher? A college professor? A senior center arts instructor? Do you teach ESL or advanced physics? There is no one certification that qualifies a "teacher" unlike the "RN" licensure.
So maybe the different kinds of nursing ought to have their own separate training programs. Maybe they train together the first term or take some classes together, but otherwise they are separate degrees. The different areas of nursing would then have to more clearly define themselves publicly and within itself as a profession. Acute care nursing education would include most bedside hospital nursing. This nursing involves fairly quick patient turnover and immediate physiologic monitoring and intervention. Long term care nursing education could include training for nursing homes, long term inpatient rehab, etc. They'd learn to deal with a larger patient load and the type of charting for this type of environment. More emphasis would be placed on preventing patient deterioration. Community health nursing education then would focus on public health and perhaps generic school health. If a nurse wanted to change fields, they could take a shorter course to qualify for a different field of nursing.
Home health needs would dictate what type of nurse was called for... short term home chemo or a complicated home hospice patient might call for an acute care nurse whereas a more stable or less acute home patient might call for a LTC nurse.
If a school had particularly complex patients, they might need to hire an LTC nurse familiar with chronic child health conditions in addition to a community health nurse who would cover the healthy child population.
There are lots unique areas of nursing that this doesn't cover and I'm sure there are tons of flaws in my quick sketch but what do you think of the general concept?