Skirmishes are for low level players, and for players who don't know their skill within the tournament scene. To encourage new players to participate, players that come in first should be barred from playing in future skirmish events so that new players will feel more at ease thinking they can place in these tournaments, and to prevent the same people from winning these tournaments.
Participation in skirmish events has been minimal recently. A $5 or $10 cash prize to the top player may incentivize players to return to claim first, or a chance to be casted could also cause players to compete for that opportunity. Skirmish events are important for inviting new players into metaplays tournaments, such as stream lurkers, and while they haven't had the best turnout recently these tournaments have quite a bit of intrinsic value to the player base.
Perhaps new casters that join metaplays could be tasked with spectating these tournaments?
Skirmishes obviously aren't as high stakes, so unique gameplay or other attributes should be focused in order to hype up this type of tournaments. Players that do well in skirmishes feel empowered and try to compete in monthlies, just like a customer returning to a business they had a positive experience with.
There's a lot that could be done with skirmishes, it would be a shame to see them go because of low turnout.