Why don't have a little tournament, of few matches -all rounds in neutral stadium- where to involve the 14 league teams?

So basically, the top 2 would play directly in QFs so the draws can look something like:



1-to QF
8vs9th

3vs14th
6vs11th

2-to QF
7vs10th

4vs13th
5vs12th

4 Matches using the table we have after the 13th Round of league.