The 'conventional means' of defeating a Primal pretty much involves throwing numerous skilled combatants at them and hoping for the best. Many are then killed, injured or Tempered. Sure, the Warrior of Light can handle them more easily but he's not going to be around forever or even realistically available on a whim.

The Garleans, at least, are being proactive about trying to find a solution to the Primal/Eikon problem. Much like the Allagans did. You can disagree with their methods, sure, but the alternative 'solutions' aren't exactly great.

As for Hydaelyn being 'weakened' by Garlemald's actions? Even if that's the case most of the blame can rest on her for not being bloody open and honest with the WoL and Scions. Though since it's heavily implied that all is not as it seems with her it's probably premature to pin the Garleans as the bad guys just yet.