I'm having trouble with these - it feels like there's no real way to reliably punish anything.

Like, oh, the opponent committed to a move with a really long windup?
No, they didn't. Anyone can whiff cancel anything for free, so your punish won't work. In fact, the opponent is closer now, and gets to wind up THEIR attack early, and punish your punish for free.

Love the game so far, but I'm not getting this aspect. It feels like there should be more consequence to these.

EDIT: As of 0.3.0, the cost of a whiff cancel has increased to 50% of your burst bar and things feel a lot more consequential! It feels like things are in a good place now.

but that is the whole concept of yomi though. you gotta get into the mindgames of "alright i know they feinted a slow move but will probably cancel that so i have to feint a move as well but they know that so i should do...". you have to be better at "I know that you know that i know etc" stuff and know when to take a calculated risks.
I enjoy it a lot, though early matches sure involve a lot of whiff canceling chains. As i played another person for a few matches we got to the point where i outplayed or got outplayed and even whiff canceling would just not work, because we thought 3 moves ahead while the other only looked 2 moves forward. Depleting an opponents burst bar by forcing whiff cancels is a very valid move and while it does not get you a hit in now, it will ensure that they cant get out later

Also managing your cancel bar is very important so you dont get caught in a really bad spot. So IMO it is fine as it is now

so, your oppenent whiffed, and now they are going to cancel

You have a few options

A: do nothing (not completely awful, as then you have the maximum amount of time to react to whatever bull they might throw out after the cancel

B: Use a REALLY fast move to basically cancel out all their options (IIRC, you cant guard or dodge after a whiff cancel, so very fast moves (say, cowboys pommel) can make literally every possible move unsafe and guarentee a hit)

C:Play 'whiff cancel chicken' (Where you just keep whipping out moves and cancelling them until one of you cracks or runs out of burst)

At least, those are the options that go through my head, whiff cancelling makes the game special in my mind, and the entire thing becomes a very tense rock paper scissors situation.