What happens after 53k is that analog phone lines produce "cross-talk". This is where the power used in a phone line is so much that it actually interferes with communications with other lines (I'm simplifying...). I don't think new cordless phones do this much, but I know the old ones certainly did and sometimes you could do this with walky-talkies: you could pick up another conversation while you were talking - that's cross-talk. Of course, that's not due to the physical phone line but the radio transmission between the cordless phone and its base, but the idea is the same. You can imagine that it would suck really bad trying to transmit information - it would become pretty corrupted or screw with other communications, and FCC regulations forbid that for most devices (it may not cause interference, blah, blah).
DSL is different. First, though, I wanna clear up the asynchronous and synchronous thing. Synchronous DSL, which isn't common, is where the speeds are "synchronized" or the same; the upload and download speeds are the same. The DSL most common, especially to homes/residences is ADSL or asynchronous DSL. That's where the upload and download speeds are NOT the same, they are A-synchronous, or NOT synchronized. Now, about DSL: those copper wires can actually carry more frequencies, and so more bandwidth, than your voice calls. DSL takes advantage of this extra frequency left over; a lot of service will let you talk on the phone and use DSL at the same time. Why was there all this extra space anyway? Well, by using a narrow frequency range of what those copper wires are capable of, you have very low interference and can pack in a lot of copper wires in a smaller area, making stuff cheaper. The phone companies want it cheap and the FCC wants no interference... so you can see what happened.
However, your voice system uses about 0 to 4000 hz, but your copper wires are capable of up to a few million hz. Obviously, there's stuff there to exploit. It's limited in how clear the signal is, which is limited by your distance from a central telephone office. With a digital signal it's much safer to exploit this left over frequency for whatever you want, and not the interference problems like you do with an analog signal.
So... basically, you're trying to get faster than 53kbps in a very narrow frequency range, the space reserved for analog transmission. Without some AMAZING data compression techniques, there's just not much space to squeeze out of this small frequency range and use. We pretty much use it all right now.