The top technical problem I notice in advanced students everywhere is a weak tone. To me, sound is everything. Without resonance and projection in your tone, everything you might try to express in your phrasing is obscured.
We don't always realize when we're making a poor tone. A tone that sounds quite pleasant from where we're sitting, right underneath the cello, doesn't always sound that way to the audience. That's because what sounds great under your ear doesn't necessarily project further than a few feet, and cellists are often shocked to hear on recordings that their tone is pallid and un-nuanced. That's why I suggest in Chapter 6 of Cello Practice, Cello Performance that self-recording should be part of daily practice.
What makes good tone? As I wrote in the book, intonation and vibrato are interdependent aspects of tone production, and so is the "Tone Triangle" (a term coined by one of my students) of arm weight, bow speed, and...everyone's bugbear, contact point.
Exactly why do so many advanced players hate to play close to the bridge? Even though it's been conclusively proven that this is the way to give your tone focus, resonance, and projection?
Well, because it's harder work. The string is very "tight" next to the bridge, and the greater resistance means that we need to pay close attention to keeping the arm heavy and relaxed into the string, and to controlling the bow speed so that you can get a core to the sound. It feels much easier to play further towards the fingerboard, where the resistance is less. Unfortunately, that's not where we can make our best sound.
I don't believe that apathy is the reason people aren't playing close to the bridge. I think it's actually because they've tried to do it, produced a scratching tone, and given up, making the assumption that their equipment is somehow defective.
I've seen this happen enough times that I think it's worth pointing out something incredibly simple that we don't always consider. There is a way to play on the bridge and still get a resonant core to the fundamental of the note: you just loosen your bow hair a bit.
Here's what a bow looks like when done up to its "normal" tension:
...and here's how loose it needs to be for you to play more easily on the bridge:
Many students I've shown this to regard it with horror. "But I'll hear the sound of the stick on the string if I have it that loose!" No you won't, not if you make it your "default setting" to bow close to the bridge.
As always, the key to mastering this is experimentation. Using the biggest practice space you can afford, make recordings of yourself playing with different bow-hair tensions and different contact points until you achieve the best "concert-hall tone" your equipment and your technique can produce.