Why and how is DNA synthesis so much faster then RNA synthesis in bacteria?
I wouldn't call them hypotheses, but the question is intriguing, and, as it seems to be ignored in the literature, I'll make a couple of suggestions. 


Perhaps it has something to do with recognition of termination signals in relation to selective pressure for speed in the two processes. 


Perhaps if elongation of the RNA chain were any faster it wouldn't be able to respond to the rho-independent termination signals which are thought to be specific stem–loops in the DNA that cause the RNA polymerase to pause and fall off the DNA. The speeding RNA polymerase might disrupt the loops instead. The termination system for DNA replication may have evolved to be much more robust so as to be able to bring faster elongation to a stop. (Note: my suggestion of different ‘robustness’ in termination is not based on any data, it's pure speculation.)

If this were true, it would beg the question of why transcription hasn't evolved a more efficient termination system in concert with the a evolution of a smarter RNA polymerase. Perhaps the answer here is that there is no selective pressure for faster transcription — the rate is clearly sufficient to supply the needs of the cell — whereas the rate of DNA replication determines the time between cell divisions and thus the rate of growth, which is subject to selective pressure.


Perhaps it has something to do with error frequency in relation to selective pressure for speed in the two processes.


First I'll make it clear that I think the proofreading argument in the question is a bit of a red herring. If the rate replication is 20x as fast as transcription, the occasional backtracking will not have much effect on the overall difference. However errors and proofreading could be involved in a different explanation. 

RNA transcription does not have proof-reading. The length of RNA transcripts is such that the cell can tolerate the errors that occur. However if the speed transcription were increased it is reasonable to expect an increase in error frequency, which might be detrimental. The current rate of transcription may be a trade-off between efficiency and accuracy. Of course one can imagine a proof-reading system for transcription evolving if it were necessary, but, as discussed above, if the rate of transcription is adequate there would seem to be no selective pressure to produce.