The rule doesn't state that flights in controlled airspace, or any flights for that matter, must be from fixed sites.
Ҥ 44809. Exception for limited recreational operations of unmanned aircraft
“(a) In General.—Except as provided in subsection (e), and notwithstanding chapter 447 of title 49, United States Code, a person may operate a small unmanned aircraft without specific certification or operating authority from the Federal Aviation Administration if the operation adheres to all of the following limitations:
(1) through (4) blah, blah, blah
“(5) In Class B, Class C, or Class D airspace or within the lateral boundaries of the surface area of Class E airspace designated for an airport, the operator obtains prior authorization from the Administrator or designee before operating and complies with all airspace restrictions and prohibitions. [This is where LAANC will be used]
(6) to (8) blah, blah, blah
Next section
“(b) Other Operations.—Unmanned aircraft operations that do not conform to the limitations in subsection (a) must comply with all statutes and regulations generally applicable to unmanned aircraft and unmanned aircraft systems. [This allows other flight opportunities but the operator must be really familiar with all the rules.]
Next section - applies to flying from a fixed site, not that you must fly from a fixed site. It says if you're flying to the rules of section(a) above AND at a fixed site, you follow this section. This allows flight in controlled airspace at known locations, without the need for getting additional approval, i.e. using LAANC, because the site location would be "pre-approved." Having pre-approved areas was a goal during the creation of the model aircraft rules, so that the operator wouldn't have to contact the airport/ATC each time. As reflected in some of the posts on this forum, some operators were allowed to fly at their "home area" without making contact each time.
“(c) Operations At Fixed Sites.—
“(1) OPERATING PROCEDURE REQUIRED.—Persons operating unmanned aircraft under subsection (a) from a fixed site within Class B, Class C, or Class D airspace or within the lateral boundaries of the surface area of Class E airspace designated for an airport, or a community-based organization conducting a sanctioned event within such airspace, shall make the location of the fixed site known to the Administrator and shall establish a mutually agreed upon operating procedure with the air traffic control facility.