Disclaimer: I work for an SEO agency.
Scaling is a challenging thing, but as with any other company it depends on the growth of the company itself. If the company is not gaining clients then there is no real need to grow. But let's assume that the company is growing and gaining clients at a brisk pace.
How to scale: Finding people who are actually qualified in SEO is tough. Each firm does things differently (White Hat vs Black Hat). The best way to over come this dearth in talent, is to actually train people who want to learn and have a passion for SEO. If you time it right you will have a cycle going so that once the pupil turns to master there will be sufficient clients for that person to handle on their own.
While they are in training you are able to pass on the tasks that take a lot of time and are less client facing (implementation, link building, report generation, etc).
This allows your master to spend time developing the strategy and training the student.
Automation: There are tons of tools to help in various aspects. As for the program you mention, stay away. That is unless you want to see short term results and unhappy clients. The true gains in automation come from not building out crappy links, but by increasing your ability to produce meaningful results thru efficiency gains of repetitive tasks. While that program helps you do that in the short term, it is not a long term solution.
An example of a true gain would be as simple as automating your reporting and monitoring of the various signals that are important in SEO.
As a side note, some of those Large SEO companies who do what you say, may not be so large ;). They may be doing that because either they limited resources or don't know how to do it the right way.