That's not what the tables and text in LBB3 (pp.14-15 & p.17) say. At the very least they tell us that low TL worlds are importing pre-built drives and computers. More likely in my experience the Referee will interpret this as meaning that a low TL A starport can't build a ship with those big drives unless they're specially imported by the PCs, if then.
LBB:3 does not matter for ship building. Pick up LBB:2 and find a reference to local world TL - there isn't.
"Shipyards:
Any class A starport has a shipyard capable of starship construction
located adjacent to it. Any class A or B starport has a shipyard capable of constructing
non-starships. In most circumstances, shipyards are quite willing to construct
and sell ships at standard prices. In some locations (throw 11+ to occur) a local government
will prohibit the construction of military or armed vessels."
"3. Routine Maintenance. Annually, a starship should be given a complete overhaul
in order to insure that it is kept in good working order. Such maintenance costs
0.1% (1/1000th) of the cash price of the ship,
and requires two weeks at a class A or B
starport."
There are many worlds in canon that don't have the TL to construct drives, and yet have type A starports and can build ships.
Similarly there are a lot more worlds with type B starports and a TL less than 9 yet they can perform annual maintainable.
"Space ships are constructed and sold at shipyards throughout the galaxy.
Any
class A starport has a shipyard which can build any kind of ship, including a starship
with jump drives; any class B starport can build a small craft and ships which do
not have jump drives. The military procures vessels through these yards, corporations
buy their commercial vessels from these shipyards, and private individuals
can purchase ships that they have designed through them as well.
The major restriction
on the purchase of ships is money."
A change to the local world TL being a factor would require minimum world TL based on starport class of 9, and that is not how the system works, or the removal over every A and B class port from a world TL8 or less.