My immediate feeling is that it just wouldn't be financially viable to do on a national scale outside of the tournament at Lincoln. Apart from the A tournament the provinces tend to just organise fixtures between themselves both pre-season and during the season. Neither the provinces nor NZC have the cash to fund what you've suggested I don't think.
Availability would be a pretty major issue too I suspect, most blokes have normal 9-5 jobs unless they're still studying. I imagine that's why the A tournament is held right at the end of the holiday season so more guys are available.