-based implies that the place is a base for operations that take place across a wider region. In Abbott’s case, worldwide. Without based, there is a possibility that Abbott Park is the only place the company impacts. One would not generally say of a mom and pop sandwich shop that it is -based. Because a company whose agents operate far and wide and report back on the base or headquarters, deserves a -based.

If you take -based away the meaning will not really change, but ambiguity with respect to region of impact will be possibly introduced.

When some place names are used in company name, based resolves ambiguity between name and location.

Technical term is “headquartered in.”