As others have mentioned, making recruiting truely national would likely leed to a lot of kids getting 20K thrown at them out of the gate like we currenlty have. It could almost become an all or nothing strategy.
Say I've got 4 openings at an A- prestige school. Typically that would be a fairly strong position, not the best, but certainly not the worst or even average any given season. W/ those 2 openings, I need 1 post and 1 SG, plus 2 other kids that can ride the bench a season until upperclassmen move on. So I target a PF in Arizona and a SG in Ohio and drop 5K first cycle, each, only to find that someone is going to come strong after those kids, so I quickly move on dropping another 5k elsewhere on 2 different kids to see someone else come after them, and so it goes, quickly burning thru money cycle after cycle until I find my comfort zone.
Conversely, you decide to sit out a cycle or 2 and see what the landscape looks like, well now in order to get the top end kids, you're going to have to go strong and hard, and likely waste the other 2 spots. I think either way, you'd see a lot of programs end up w/ 2-3 walkons each year so they could battle coast to coast. Perhaps not a bad thing, but in the end I think it would make recruiting much more difficult, time consuming and ultimately fustrating. Luck would play an even bigger roll than it does now.
As it stands right now, you can reasonable predict who might target the same kids you're going to. In a nationwide deal, it would be almost impossible to predict. It would be nothing for a school to come in late w/ 3 openings, drop everything into 1 of your kids while you're working to fill out the back of your roster and leave you with nothing. This can still happen today, but has a much smaller chance as the number of schools that can do this is limited to your geographical region. Nationwide recruiting, under the current landscape would turn into a blood bath.
If it were to work, I almost think it would have to work something like what EA sports NCAA football recruiting did. An initial wave each week of the season to slowly build up support/interest in several kids, then a concentration to battle things out. You'd need time for kids to formulate a list of competitors for their services, perhaps decide upon their 5 official visits then select the school that recruited them the best, has more playing time, more prestige, etc.... I think it's certainly possible to create an atmosphere like that, and make it work, but I imagine it would take a ton of programming.
As I mentioned earlier, I don't think the current system is too bad, and creates some equity w/n the game, keeps power programs w/n check to an extent and also creates some diversity in recruiting. I've got 2 D1 teams in Crum, Texas & Georgetown and recruiting is very different. I've been an A level prestige (A- thru A+ depending on the season) for awhile now, and at Texas once recruits are spread out thru LSU, Texas & Texas Tech w/ the occasional battle from Oklahoma, Kansas, Arkansas or elsewhere, things don't change. If you lead by noon of the 2nd day, you rarely see a late charge, things are pretty easy as long as I pay attention to the needs of LSU, TT and others and make sure the places I'm targetting don't conflict w/ their targets if they've got more "power" than me, and vice versa.
Meanwhile at Georgetown along the East coast, I'm often fighting w/ UVA, UNC, Duke, Penn St, Seton Hall, Marlyand, etc.. where I stand at noon on the 2nd day means nothing. Late charges are often made by not only fellow Big East or ACC schools, but also some of the mid level program in the area hoping to spot a weakness amongst the battles. In a lot of ways, its much more challenging but also more enjoying.
At Texas I might have 3 top 10 SGs one year w/n 300 miles, then I might go 3 seasons or more w/o a top 10 SG w/n 300 miles. At Georgetown there's going to be a top 10 player at every position each and every season w/n 300 miles, but there are also going to be multiple schools wanting to fill the position in the area each and every season.
At Texas I might ignore the #3 SG who looks like a stud to focus on the #8 SG that looks solid, just a step below but I know can fill in at PG in case there are no decent PG recruits the following season or 2. Flexability is a huge asset in recruits. At Georgetown, I'm going after the stud each time b/c I know there will be multiple solid PGs if I really need one the following season. Flexability doesn't mean nearly as much.
Meanwhile, a school like Hawaii offers a completely different challenge. If nationwide recruiting truely existed, all schools would essentially become the same more or less. It would take some variety away from today's game. Some coaches like the challenge of a big market w/ lots of big fish, others like being out in the middle of no where having to go long distances to find a hidden gem or 2 each season. If recruiting at Georgetown was identical to Texas, I'd likely would have dropped one or the other by now. However the different aspects and challenges of each school has made the world a little more interesting to me.