Actually, I think the problem may be that they didn't go all the way. If overhead space also cost, then it wouldn't be the scarce free resource everyone fights over. A much cheaper cost for checking small items (backpack, over the shoulder bag) and very close to parity with checked items (maybe above, maybe below) for suitcase sized items would likely solve the problem. A slight reduction in fees for checked bags would also be warranted.
Once everything is accurately priced and tracked, there's no problem with space anymore. They know how many cubic feet of space they have, and they know what they've charged for.
Do you really think so? I imagine a $100 ticket would go to something like $97, and there might be a $5 fee for a small overhead space (regular size purse), $10, for a medium space (backpack or large purse), and $15-$20 for small luggage, and then going up steeply from there (since you should be checking things that size). Checked baggage prices might drop by $5 or so too, since they aren't subsidizing free overhead space.
Free additionals that have direct cost to the the provider but may or may not be useful or utilized by the customer are things for luxury products. Overall, everyone is better off (even if they don't feel better off) by paying for what they actually use. The people that lose out are the people that used to use more than their fair share. If you still like the idea of paying one (higher) price and having things like luggage covered, that's what other classes (like premium economy, business and first class) are for. It's called economy class for a reason...
I'm talking about "transaction costs" in the economics sense - the cost to the company of tracking who's paid for what, to the customer of comparing complex pricing schemes, etc.
No one likes getting nickled and dimed. While they are at it, weigh everyone before boarding, to properly charge them for how much extra fuel they consume beyond the base charge. Then heavier people won't be using more than their "fair" share. Except now you've pissed off even the super skinny people who have to deal with the "transaction cost" / extra time involved, who were perfectly willing in the past to perhaps pay slightly more than if they were heavier because it simplifies the experience. Heavier people also think that way, not "oh boy I'm getting a good deal flying at the same price as this lightweight".
Indeed, that works great for all the people who pack and measure exactly their bags a month in advance when they buy their ticket so they know the exact dimensions.
In reality, no one knows the dimensions of their bags until the night before, and that's too late for the airline to tell them "no" or add charges reasonably.
Once everything is accurately priced and tracked, there's no problem with space anymore. They know how many cubic feet of space they have, and they know what they've charged for.