Attaching speaker wire directly to crossover?

That is undoubtably the best approach but a little hair shirt even for an audio nut like me. A good intermediate step is to look at the quality of the posts, internal wiring and connectors being used and replace them if necessary. I have been upgrading my Spendor S 100s. I had the internal wiring changed, used better connectors to the bass and mid and am changing the posts. The posts fasten directly to the crossover so I couldn't use the ones I had on hand, they were too big to go through the hole in the circuit board. In most speakers the posts are easy to change and will often make a considerable improvement. Wire does also, I was going to use all Cardas but they shipped me the wrong quantity for the tweeter so I substituted solid silver on it. Result is very detailed but a little too bright.
If you are really dedicated hard wire is always the way to go but lesser steps will get better sound , removing the crossover from the speaker inclosure will also help but all of these will alter the sound in ways that are difficult to predict. See my experience above.

Changing out the binding posts from an inexpensive factory stock to a decent quality set such as Superior Electric's, Vampire's, etc...can make a world of improvement. I personally would not consider wiring directly unless the spks were very, very inexpensive. Bill

Hey all - a belated thanks for these responses. I guess it's an interesting idea if you've already vetted how a given wire sounds when connecting a given amp and speakers, although I do wonder whether connecting the wire directly to the crossover wouldn't be a significant additional factor to consider that could end up changing your choice of wiring!

Dan ed - I'm guessing the upgrade on those GMA's was $2200 because it included the price of the wires themselves.