I'm not certain thats the best solution but im not opposed to trying it either. A first round match between Urhan and Adrigole is a very different proposition in terms of travel than Urhan and Mallow. You'd do it for a final or semi but earlier rounds could see fewer people attend than would now.
Rather than a fully open one, you could try a middle ground. Maybe for the first round or two group (or amalgamate) the divisions like the league suggestion and then once you've had a few local games send the winners forward to the open draw. The remaining teams would have abit of momentum behind them so should be a better incentive for people to travel and you still get a very decently varied pot of teams to play in the middle and late rounds.
Rather than a fully open one, you could try a middle ground. Maybe for the first round or two group (or amalgamate) the divisions like the league suggestion and then once you've had a few local games send the winners forward to the open draw. The remaining teams would have abit of momentum behind them so should be a better incentive for people to travel and you still get a very decently varied pot of teams to play in the middle and late rounds.