If everything stays at 12V, just a boost is not good enough as there is also a load dump situation when the input voltage can fly up as high as 100V (with TVS clamp it can also be around 40-60V) so a 12V system indeed is not a 12V system. So I don't think a boost converter boosting the input o 12V or 24V (for audio as mentioned in the article) helps. Fortunately, most electronics run at much lower voltage (3.3V, 5V etc.) so there is a high voltage buck after the so-called 12V rail. However, if a real robust 12V is needed, people have to consider the buck-boost or SEPIC design.
Not sure what you mean by "main battery". I believe this article is addressing simple, stop-start only, micro-hybrid vehicles (not mild or full hybrid vehicles which have a secondary high voltage battery). These micro-hybrid vehicles typically use a single 12V lead-acid battery, often an AGM for better cycle life. They are prone to voltage sag during starting since the starter (either an enhanced cranking motor or a Belted-Alternator-Starter or an Integrated Starter Generator) rely on the 12V battery for cranking energy.
Mild or full hybrids with a secondary high voltage battery all use the high voltage battery for re-starting and therefore do not have the voltage sag problem during re-starts.
Certainly a bigger battery would help, but it is a trade-off between a bigger battery and a DC-DC boost converter. The bigger battery will still have voltage sag during cranking which may be noticed by the customer in the form of dimming lights, slower blower speeds, etc.
The big difference here is that during a normal start the electrical accessories are (intentionally) turned off. During stop-start the accessories are still active and one of the goals is to make the stop-start function as transparent to the customer as possible.