tl;dr: because government agencies don't operate under those kinds of constraints
Take a step back: why should new technology require fewer staff? If technology make staff more efficient, do you fire the (now extra) staff or move them to some other kinds of tasks?
Firms are interested in earning profit. Efficiency gains lower costs and result in more profit. So for a firm it makes sense to replace staff with technology. They lower costs and earn more profits.
Governments don't work this way. A government agency has a set amount of money it can spend [ Young, 2006]. Efficient agencies don't have larger budgets than inefficient agencies - they are just able to do more with their resources. So when an agency becomes more efficient (such as by introducing new technologies) it will usually those resources. For staff, this generally means keeping roughly the same number of positions, even though positions may be moved between functions. Realistically, even if an agency did cut staff due to technological improvements, it would likely use that money to hire other staff for other programs.
Kernaghan and Gunraj (2004) discuss one particular way this occurs: increased efficiency due to technology also drives staff specialization. Agencies may retrain staff to allow them to specialize rather than fire them.
Finally, an agency in most cases must spend it's entire budget in a year [ also Young, 2006]. If an agency were to cut positions and save money, it would have a lower budget next year. This is also different from private firms: there is a disincentive to cut overall costs.
Is this bad? A commentor suggested this answer is prejudiced against government employees. However, this answer shows why a rational, intelligent manager of a public agency would not cut staff even when technology makes them more efficient. Basically, that would mean paying costs (in terms of a lower budget in future years) and receiving no benefit.