I understand multiple origin bubbles; DNA polymerase only synthesizes DNA from 5' to 3' and all that. But what I don't understand is why it has to be in fragments. Yes, DNA is anti parallel, and so the DNA elongates in opposite directions, since DNA polymerase can only go one way. But why not go on just like the leading strand? Why not continue happily along the DNA template continuously but in fragments?
I think you may have been misled by graphic representations of the process: The actual replication fork is very small as, like Rex Kerr mentions, it costs a lot of energy to keep DNA single stranded.
Have a watch of https://www.youtube.com/watch?v=yqESR7E4b_8 at minute 1:45, it contains a relatively realistic representation of the replication fork. Of course you have to imagine all of the space around the molecules in this video to be filled with other DNA, RNA, proteins and small molecules zipping about.
On top of this, we like to think of DNA as a lone double strand where occasionally a protein might attach and do something. Realistically however, most of the DNA is constantly being manipulated by all sorts of proteins (mostly histones for compression, but also transcription factors, methylating and demethylating enzymes, DNA repair enzymes,...). DNA replication has to minimise the interruption it causes to all the mechanisms going on around it, and the most effective way to do this is by replicating the lagging strands in fragments which can be zipped up quickly and left to whatever other proteins might do to it.
It's in fragments for efficiency. Single-stranded DNA is not very stable without proteins to stabilize it. If you tried to replicate the entire strand in one go, you'd need to keep the entire strand in single-stranded form one way or another (e.g. start at both ends and meet in the middle would still leave each half as an old/new duplex, plus an old single-stranded copy waiting to be filled in from the other direction).
To avoid needing a chromosome or genome's worth of SSDNA binding proteins, it works in fragments.
(That is: if you had organisms that had to produce that much SSDNA binding protein, they'd be out-competed by organisms that didn't have to.)