Can I convert my dozens of laptop adapters into universal ones by using RJ-11 or RJ-45 connections?
Short answer: not like that.
Long answer: RJ11/RJ45 (aka 8p8c) connectors aren't made for delivering power.  PoE is a bit of a kludge that uses higher voltages to reduce the current to what can go through a jack and the cable, maybe an amp or two through your garden-variety connectors.  If you want an easy higher-power connection, use a barrel connector.  Bonus: it will be easier to hook up to the ~16AWG coax cable that comes out of most power bricks (that's another thing, most of the 8p8c connectors top out at the 24-22AWG range).
The thing you have to watch with the bricks is that some of them have some proprietary signalling between them and the device being powered to ensure that they're compatible.  I suspect that half of this is legitimately to prevent someone from using a cut-rate brick they got off of who knows where and damaging something.  I suspect the other half is so that Dell or whoever can charge you an arm and a leg for a replacement.