Adding the feedback resistor moves the integration up to some higher frequency as discussed in the linked article. That simply won't work for analog computing where signals (variables) are slow moving. I want to be able to change 10V is 1 second or if the problem scales to 10x, I need 10V in 0.1 second. AFAICT with my limited knowledge of analog computing, these are the highest frequencies involved. In other words, right down to 0 Hz.
With the added resistor, all you have is a fancy low pass filter.
Offset voltage can often be nulled out by using the 'trim' pins on the op amp.
http://www.analog.com/media/en/training-seminars/tutorials/MT-037.pdfThe next analog computer I build will have the capability of adjusting the offset voltage. I'm generally dealing in volt level signals so I'm not sure how important some number of microvolts really is. It's not like the simulations last very long so there really isn't enough time for the offset voltage to impact the results. And let's face it, I'm not dealing with high resolution. 'About' is good enough. If you have seen one damped harmonic motion, you have pretty much seen them all.